



















PECLASSiriBD 
By aiitliwity Swntary ot 

SEP 14 1960 

Oefenae memo 2 August 1960 
IIBSABY OF CONOKE8S 






By 


St? \ 41960 





SUMMARY TECHNICAL REPORT 
OF THE 

NATIONAL DEFENSE RESEARCH COMMITTEE 



This document contains information affecting the national defense of 
the United States within the meaning of the Espionage Act, 50 U. S. C., 
31 and 32, as amended. Its transmission or the revelation of its contents 
in any manner to an unauthorized person is prohibited by law. 

This volume is classified in accordance with security 

regulations of the War ana- r»vaAy-lJgp^tn^ because certain chapters 
contain material which was’^MI at the date of printing. 

Other chapters may have had k-Ua^er classification or none. The reader 
is advised to consult the War and Navy agencies listed on the reverse 
of this page for the current classification of any material. 



Manuscript and illustrations for this volume were prepared 
for publication by the Summary Reports Group of the 
Columbia University Division of War Research under con- 
tract OEMsr-1131 with the Office of Scientific Research and 
Development. This volume was printed and bound by the 
Columbia University Press. 

Distribution of the Summary Technical Report of NDRC 
has been made by the War and Navy Departments. Inquiries 
concerning the availability and distribution of the Summary 
Technical Report volumes and microfilmed and other refer- 
ence material should be addressed to the War Department 
Library, Room lA-522, The Pentagon, Washington 25, D. C., 
or to the Office of Naval Research, Navy Department, Atten- 
tion : Reports and Documents Section, Washington 25, D. C. 

Copy No. 

238 


This volume, like the seventy others of the Summary Tech- 
nical Report of NDRC, has been written, edited, and printed 
under great pressure. Inevitably there are errors which have 
slipped past Division readers and proofreaders. There may 
be errors of fact not known at time of printing. The author 
has not been able to follow through his writing to the final 
page proof. 

Please report errors to : 

JOINT RESEARCH AND DEVELOPMENT BOARD 
PROGRAMS DIVISION (STR ERRATA) 

WASHINGTON 25, D. C. 

A master errata sheet will be compiled from these reports 
and sent to recipients of the volume. Your help will make 
this book more useful to other readers and will be of great 
value in preparing any revisions" 



SUMMARY TECHNICAL REPORT OF DIVISION 7, NDRC 


VOLUME 3 


AIRBORNE FIRE CONTROL 


DECLAssrpniin 

By authority Secrstaty d 

SEP 141960 

Defense memo 2 August 1960 

library congress 

OFFICE OF SCIENTIFIC RESEARCH AND DEVELOPMENT 
VANNEVAR BUSH, DIRECTOR 

NATIONAL DEFENSE RESEARCH COMMITTEE 
JAMES B. CONANT, CHAIRMAN 

DIVISION 7 
H. L. HAZEN, CHIEF 



WASHINGTON, D. C., 1946 


NATIONAL DEFENSE RESEARCH COMMITTEE 


James B. Conant, Chairman 
Richard C. Tolman, Vice Chairman 
Roger Adams Army Representative^ 

Frank B. Jewett Navy Representative- 

Karl T. Compton Commissioner of Patents^ 

Irvin Stewart, Executive Secretary 


'^Army Representatives in 07'der of service: 
Maj. Gen. G. V. Strong Col. L. A. Denson 

Maj. Gen. R. C. Moore Col. P. R. Faymonville 

Maj. Gen. C. C. Williams Brig. Gen. E. A. Regnier 
Brig. Gen. W. A. Wood, Jr. Col. M. M. Irvine 
Col. E. A. Routheau 


-Navy Representatives in order of sei'vice: 

Rear Adm. H. G. Bowen Rear Adm. J. A. Purer 

Capt. Lybrand P. Smith Rear Adm. A. H. Van Keuren 

Commodore H. A. Schade 
^Co7mnissioners of Patents in oi'der of service: 
Conway P. Coe Casper W. Corns 


NOTES ON THE ORGANIZATION OF NDRC 


The duties of the National Defense Research Committee 
were (1) to recommend to the Director of OSRD suitable 
projects and research programs on the instrumentalities 
of warfare, together with contract facilities for carrying 
out these projects and programs, and (2) to administer 
the technical and scientific work of the contracts. More 
specifically, NDRC functioned by initiating research 
projects on requests from the Army or the Navy, or on 
requests from an allied government transmitted through 
the Liaison Office of OSRD, or on its own considered 
initiative as a result of the experience of its members. 
Proposals prepared by the Division, Panel, or Committee 
for research contracts for performance of the work in- 
volved in such projects were first reviewed by NDRC, and 
if approved, recommended to the Director of OSRD. Upon 
approval of a proposal by the Director, a contract permit- 
ting maximum flexibility of scientific effort was arranged. 
The business aspects of the contract, including such 
matters as materials, clearances, vouchers, patents, pri- 
orities, legal matters, and administration of patent mat- 
ters were handled by the Executive Secretary of OSRD. 

Originally NDRC administered its work through five 
divisions, each headed by one of the NDRC members. 
These were: 

Division A — Armor and Ordnance 
Division B — Bombs, Fuels, Gases, & Chemical Problems 
Division C — Communication and Transportation 
Division D — Detection, Controls, and Instruments 
Division E — Patents and Inventions 


In a reorganization in the fall of 1942, twenty-three 
administrative divisions, panels, or committees were 
created, each with a chief selected on the basis of his 
outstanding work in the particular field. The NDRC mem- 
bers then became a reviewing and advisory group to the 
Director of OSRD. The final organization was as follows: 


Division 1 — Ballistic Research 
Division 2 — Effects of Impact and Explosion 
Division 3 — Rocket Ordnance 
Division 4 — Ordnance Accessories 
Division 5 — New Missiles 
Division 6 — Sub-Surface Warfare 
Division 7 — Fire Control 
Division 8 — Explosives 
Division 9 — Chemistry 
Division 10 — Absorbents and Aerosols 
Division 11 — Chemical Engineering 
Division 12 — Transportation 
Division 13 — Electrical Communication 
Division 14 — Radar 
Division 15 — Radio Coordination 
Division 16 — Optics and Camouflage 
Division 17 — Physics 
Division 18 — War Metallurgy 
Division 19 — Miscellaneous 
Applied Mathematics Panel 
Applied Psychology Panel 
Committee on Propagation 
Tropical Deterioration Administrative Committee 



iv 




NDRC FOREWORD 


A s EVENTS of the years preceding 1940 revealed 
L more and more clearly the seriousness of the world 
situation, many scientists in this country came to 
realize the need of organizing scientific research for 
service in a national emergency. Recommendations 
which they made to the White House were given 
careful and sympathetic attention, and as a result the 
National Defense Research Committee [NDRC] was 
formed by Executive Order of the President in the 
summer of 1940. The members of NDRC, appointed 
by the President, were instructed to supplement the 
work of the Army and the Navy in the development 
of the instrumentalities of war. A year later, upon the 
establishment of the Office of Scientific Research and 
Development [OSRD], NDRC became one of its units. 

The Summary Technical Report of NDRC is a 
conscientious effort on the part of NDRC to sum- 
marize and evaluate its work and to present it in a 
useful and permanent form. It comprises some seventy 
volumes broken into groups corresponding to the 
NDRC Divisions, Panels, and Committees. 

The Summary Technical Report of each Division, 
Panel, or Committee is an integral survey of the work 
of that group. The first volume of each group’s report 
contains a summary of the report, stating the prob- 
lems presented and the philosophy of attacking them, 
and summarizing the results of the research, develop- 
ment, and training activities undertaken. Some vol- 
umes may be “state of the art” treatises covering sub- 
jects to which various research groups have contrib- 
uted information. Others may contain descriptions of 
devices developed in the laboratories. A master index 
of all these divisional, panel, and committee reports 
which together constitute the Summary Technical 
Report of NDRC is contained in a separate volume, 
which also includes the index of a microfilm record of 
pertinent technical laboratory reports and reference 
material. 

Some of the NDRC-sponsored researches which had 
been declassified by the end of 1945 were of sufficient 
popular interest that it was found desirable to report 
them in the form of monographs, such as the series on 
radar by Division 14 and the monograph on sampling 
inspection by the Applied Mathematics Panel. Since 
the material treated in them is not duplicated in the 
Summary Technical Report of NDRC, the mono- 
graphs are an important part of the story of these 
aspects of NDRC research. 


Sumiiir 
SIP 141960 

tkSmt I Auifuil im 

In contrast to the 

of widespread interest and much of which is released 
to the public, the research on subsurface warfare is 
largely classified and is of general interest to a more 
restricted group. As a consequence, the report of Di- 
vision 6 is found almost entirely in its Summary 
Technical Report, which runs to over twenty volumes. 
The extent of the work of a Division cannot therefore 
be judged solely by the number of volumes devoted 
to it in the Summary Technical Report of NDRC: 
account must be taken of the monographs and avail- 
able reports published elsewhere. 

The Fire Control Division, initially Section D2 
under the leadership of Warren Weaver and later 
Division 7 under Harold L. Hazen, made a significant 
contribution to an already highly developed art. It 
marked the entrance of the civilian scientist into what 
had hitherto been regarded as a military specialty. 

It was one of the tasks of the Division to explore 
and solve the intricate problems of control of fire 
against the modern military aircraft. Gunnery against 
high-speed aircraft involves fire control in three di- 
mensions. The need for lightning action and superla- 
tively accurate results makes mere human skills hope- 
lessly inadequate. The Division’s answer was the 
development of the electronic M-9 director which, 
controlling the fire of the Army’s heavy AA guns, 
proved its worth in the defense of the Anzio Beach- 
head and in the protection of London and Antwerp 
against the Nazi V-weapons. In addition to producing 
mechanisms such as the M-9, the Division made less 
tangible but equally significant contributions through 
the application of research methods which had a pro- 
found, even revolutionary, influence on fire control 
theory and practice. 

The results of the work of Division 7, formerly 
Section D2, are told in its Summary Technical Report, 
which has been prepared at the direction of the 
Division Chief and has been authorized by him for 
publication. It is a record of creativeness and devo- 
tion on the part of men to whom their country will 
always be grateful. 

Vannevar Bush, Director 
Office of Scientific Research and Development 

J. B. CONANT, Chairman 
National Defense Research Committee 



REGULATION: BEFORE SERVIC^ 
^EPRODU'^’NG AN " PART OF THIS 
;CUMEN r. ALL C -ASSIFICATIOT 
\BKTNas MUST BE CANCELLEP^ 


V 




FOREWORD 


V OLUME 3 of Division 7, the Summary Technical 
Report of Section 7.2, NDRC, contains three 
parts. In Part I on aiming controls in aerial ordnance, 
Mr. G. A. Philbrick discusses the work of the Section 
in all fields except that of gunnery and the assessment 
of gunnery devices. Mr. A. L. Ruiz has contributed 
Part II, in which developments in aerial torpedo 
directors subsequent to those in which Mr. Philbrick 
took part are discussed. The third principal part of 
the report is that on aerial gunnery and assessment, 
written by Professor J. B. Russell. 

It is indeed fortunate that such a large part of this 
work could be written by one individual, who could 
thus provide a unity of treatment which otherwise 
would be very difficult to obtain. In assuming re- 
sponsibility for his part of the Summary Technical 
Report, Mr. Philbrick took on a heavy task — and 
discharged it with zeal. Under the circumstances a 
more conventional report would have fulfilled all the 


requirements, but Mr. Philbrick has served his reader 
a tasty dish of skilled technical exposition. We can 
ask no more. 

In general the part contributed by Professor Russell 
stresses the instrumental features of aerial gunnery, 
and relies upon the writing of Dr. Paxson, in Volume 
2 of the Summary Technical Report of the Applied 
Mathematics Panel, for the basic mathematical sub- 
stance of the subject. Professor Russell brings to his 
treatment continuous experience in the field dating 
from before Pearl Harbor. He has participated in all 
of its growth, first as a Technical Aide in Section 7.2, 
and during the closing months of the war as an 
Expert Consultant to the Secretary of War. 

H. L. Hazen 
Chief, Division 7 

S. H. Caldwell 
Chief, Section 7.2 




SIS 




\ 






< AP' 










CONTENTS 


CHAPTER PART I PAGE 

AIMING CONTROLS IN AERIAL ORDNANCE 
By G. A. Philbrick 

Prefatory Comments 3 

1 General Theory of Aiming Processes .... 9 

2 On Certain Aspects of Tracking 23 

3 Technology of Rotation in Space 35 

4 Simulation as an Aid in Development ... 48 

5 Linkages for Computation and Manipulation . 66 

6 Aiming of Torpedoes from Airplanes .... 79 

7 Aiming of Bombs from Airplanes 95 

8 Control of Guided Bombs 112 

9 Aiming of Rockets from Airplanes .... 133 

10 Integrated Equipment for the Pilot .... 147 

PART II 

AERIAL TORPEDO DIRECTORS 
By A. L. Ruiz 

Prefatory Comments 163 

11 Course Stabilization 165 

12 Present-Range Type Torpedo Detectors . . . 167 

13 Torpedo Directors for Use Against Evading 

Targets 169 

PART III 

AERIAL GUNNERY 
By J. B. Russell 

Prefatory Comments 177 

14 General Survey of Aerial Gunnery . . . 179 

15 General Principles 185 

16 Local Control Systems 192 

17 Remote-Control Systems 198 

18 Tracking and Ranging 204 

19 Simulation and Gunnery Assessment .... 209 

20 Discussion on Future Work 214 

Appendix 217 

Glossary 231 

Bibliography 233 

Index 245 


Confidential \ 





PART I 


AIMING CONTROLS IN AERIAL ORDNANCE 


By G. A. Philbrick 


iCONFIDENTIAL 



PREFATORY COMMENTS 


GENERAL 

D uring the past three years and a half the 
present writer has served as technical aide 
to S. H. Caldwell, Chief of Section 7.2, whose 
section has been charged with airborne develop- 
ments within the more general fire control 
framework of Division 7 of National Defense 
Research Committee [NDRC]. By delegation 
from the section chief, the writer has shared, 
with other technical aides and section members, 
several domains of responsibility in the conduct 
of research and development on airborne fire 
controls. The initiation for such work in typi- 
cal cases occurs through a request by Army or 
Navy to Office of Scientific Research and De- 
velopment [OSRD] for a particular study of 
development ; following acceptance by the latter 
organization, which is made through agree- 
ments of the relevant section and division of 
NDRC, a program is laid out and presented as 
specification for a project to the appropriate 
contractor. Guidance of this project through 
the stages of theory or experiment, design or 
test, and the maintenance of liaison with the 
same agencies concerned, constitute functions 
of the NDRC section. Such duties have in turn 
become those of such operatives as the present 
writer, who enter personally into the technical 
phases of the development of the project as 
deeply as appears necessary or appropriate, 
and who answer to the section for the conduct 
and outcome of the work. 

SUBJECT MATTER 

By reasons of familiarity and plausibility, the 
material treated in the following pages is 
naturally restricted to those branches of air- 
borne fire control with which the writer has 
been concerned at first hand. Although rather 
generously distributed over the field, these 
branches have not been all inclusive. They are 
considered sufficiently pervasive, however, to 
warrant the title given to the present report. 
In particular, the subject matter revolves about 
the development of computors and computing 


sights for aerial torpedoing, bombing, and 
aerial rocketry, with a final attempt to combine 
all of these functions with that of fixed gunnery 
for the fighter airplane. The most impressive 
omission is that of flexible gunnery, for while 
the writer has been exposed to and has gained 
familiarity with the equipment and develop- 
mental procedures in this branch, he has had 
little or no tangible responsibility there. An- 
other characterization of the present material 
refers to the character, or technical position, 
of the researches which are reported upon, and 
reflects the corresponding nature of the activi- 
ties of the writer. The latter has been substan- 
tially a creature of the laboratories, operating 
for the most part between theory and design. 
His contacts with the using Services have 
usually been with respect to a particular equip- 
ment under development, and his involvement 
with proving organizations and with aerial fir- 
ing tests has been for the specific purpose of 
gaining knowledge of the properties of one 
device rather than of a larger category. That 
is to say, the morphology of localized appara- 
tus, from the instrumental standpoint, is here 
stressed rather than a broader survey of avail- 
able ordnance or a presentation of assessment 
techniques, in spite of the recognized status of 
the latter. The flavor is thus dynamical rather 
than statistical, constructional rather than 
evaluational, instrumental rather than logistic, 
and physical rather than administrative. This 
is not to indicate any absolute preference or 
desirability, but straightforwardly to identify 
the aspect of the material to be treated, and to 
admit that this aspect stems, quite naturally, 
out of the writer’s own predilections and pro- 
pensities, quite aside from whether these are 
important. 

In addition to the description, in successive 
developmental forms, of a number of specific 
computing devices and controls, considerable 
space is here allotted to certain tools of re- 
search themselves, where it is felt that these 
constitute advances in the techniques of instru- 
ment development or design. It is believed, for 
example, that the use of increasingly compre- 


Confidential J 


3 


4 


PREFATORY COMMENTS 


hensive electronic model structures can bridge 
enormous gaps which classically have inter- 
vened between theory and concrete facilities. 
Such model structures, owing to their ability to 
“cooperate” with the real human operator and 
to incorporate discontinuities against which 
analysis is almost completely impotent, can 
bring realism to the laboratory and can shorten 
the interval over which optimum dynamics are 
attained. With completely automatic assem- 
blages the need for such models is as great 
or greater. 

As to weapons, we are concerned here with 
the airplane, the projectile, and the man at the 
firing-key, the whole group operating as a unit. 
The airplane types include principally the 
fighter, fighter-bomber, and bomber. The pro- 
jectiles are bomb, guided bomb, rocket, torpedo, 
and bullet or shell, in approximately that order 
of concern. A typical aiming control, or com- 
puting sight, involves a group of input varia- 
bles, which may be either manually or auto- 
matically introduced, a computer proper, and a 
presentation-component or sight whereby the 
aiming process is reduced to some sort of null 
between an index and the target. Automatic 
firing may be involved, either permanently or 
at the choice of the operator. 

It is difficult confidently to predict the shape 
of fire controls for the future, at least from the 
present standpoint. The trend toward more 
thoroughgoing automaticity is certainly evi- 
dent, with the task of the operator becoming 
increasingly supervisory and eclectic. At this 
level the distinctions between offense and de- 
fense, and even between strategy and tactics, 
are so interwoven with other relationships as 
to be almost nonexistent, so that we shall not 
here presume to speak of these. While the 
rocket and guided bomb, together with their 
logical combinations, are outstandingly weap- 
ons of great future significance, the bomb, 
bullet, and shell are simple structures which 
should not be ignored. As to superexplosives, 
with potentially a million times greater payload 
ratio, the need for fire control should not 
decrease any more than as between flintlock 
and main battery. While the appearance and 
character of weapons may suffer revolutionary 
changes, in whatever era, with the science even 


of orbital underwater trajectories being re- 
placed, for example, by that of underground 
trajectories, it will still be essential to direct 
and deliver fire in the vicinity of the target. 
Of the homing and automatic interception mis- 
siles on whose protection survival may depend, 
and which ultimately may truly battle among 
themselves, those with the more recondite con- 
trols will triumph along with their masters. 

COLLEAGUES 

In view of the apparent virtuosity of this 
report, the framework of personnel within 
which the writer has operated deserves par- 
ticular comment. Both categorical and special, 
the people among whom the progress herein 
reported has taken place have made it what 
it is. 

The staff of NDRC Section 7.2, with chief, 
members, and fellow technical aides, has been 
closest of all to these operations, and knows 
most about them. Thus are listed: S. H. Cald- 
well (Chief), J. B. Russell (since transferred 
to the Office of the Secretary of War), A. L. 
Ruiz, H. C. Wolfe, C. G. Holschuh, W. A. 
MacNair, E. G. Pickels, E. W. Paxson, and 
(latterly) A. F. Sise; in whose collective com- 
pany it has been an honor for the writer to 
work. Knowledge of the branches of airborne 
fire control which are not herein treated, and 
more complete discernment of those which are, 
must be sought among these gentlemen. Also 
within Section 7.2 as technical aide, R. M. 
Peters is to be mentioned by the writer as his 
staunch mathematical assistant. She has helped 
materially in every phase of progress, and is 
to be credited with whatever significant mathe- 
matics adheres to the present report. 

The remainder of Division 7, with H. L. 
Hazen as chief and K. L. Wildes as divisional 
technical aide, and with the adjacent section 
chiefs, D. J. Stewart, E. J. Poitras, and I. A. 
Getting, has served in all connections as guide- 
post and beacon. Considerable and appreciated 
interchange has been enjoyed with such mem- 
bers and technical aides of adjacent sections as 
G. R. Stibitz, L. M. McKenzie, and J. F. Taplin. 

Of other divisions of NDRC with which 
developmental business has been conducted. 


1 ^mFIDENTIA^ 


CONTRACTORS 


5 


Division 5 should be mentioned especially. Con- 
trol apparatus for new missiles has been dealt 
with in this relationship, both through an 
arranged collaboration between the two divi- 
sions, and by the writer as an officially 
appointed consultant to Division 5 itself. Con- 
structive and informative intercourse has taken 
place with H. H. Spencer, Chief, Division 5, as 
well as with J. C. Boyce, L. 0. Grondahl, 
P. Mertz, and E. W. Phelan, among others. 
Further relations have been important with 
Division 3 (F. L. Hovde) on rockets, with Divi- 
sion 4 (A. Ellett) on toss bombing, with Divi- 
sion 6 on antisubmarine warfare, with Division 
14 on radar and with Section 16.1 (T. Dunham, 
Jr.) on optical instruments. Valuable personal 
contact on professional matters has been pos- 
sible also with W. Weaver, T. C. Fry, J. D. 
Williams, M. S. Rees, and others of the Applied 
Mathematics Panel. Among other groups which 
cannot be mentioned in entirety are the admin- 
istrative and engineering staffs of OSRD and 
NDRC, both central and local. 

A detailed accounting of the Service agencies 
and personnel which have been directly con- 
cerned with these efforts would be all out of 
order in the present location. Such agencies 
and personnel will appear, however, in refer- 
ence to the project chronologies in the main 
body of the report. Relations with the Services 
have, on the whole, been extremely pleasant 
and positive. The writer’s dealings have been 
predominately with the Navy, and within Navy 
with the Bureau of Ordnance, and within 
BuOrd with the aircraft fire control sections: 
Re4 (Re4d), Re8 (Re8c). Further extensive 
affairs have been enjoyed with NAS Norfolk, 
NAF Philadelphia, NAS Squantum, NAS 
Quonset, NOTS Inyokern, NOP Indianapolis, 
and the various special devices depots, to men- 
tion only several branches. The Navy projects 
on which the writer has been engaged, and 
which are herein reported upon, include NO- 
106 (torpedo director: now TD Mark 32), 
NO-129 (antisubmarine bombsight: now BS 
Mark 20), NO-180 (maneuverable bombing 
target), NO-190 (blimp bombsight: now Mark 
24), NO-191 (bombsight presetting computer), 
NO-216 (rocket sights: now RS Mark 2 and 
RS Mark 3, and computers Mark 35 and Mark 


36), AN-4 (low altitude bombsight; BARB: 
now BS Mark 23), NA-168 (slant range com- 
puter), NO-242 (range-type torpedo director), 
NA-232 (Razon attachment for TA3 trainer), 
and NO-265 (pilot’s universal sighting sys- 
tems: now AFCS Mark 3). With the Army, we 
have dealt most directly with the armament 
laboratory (ATSC) at Wright Field, as well as 
with Langley Field, Foster and Matagorda 
Fighter Fields, Dover Air Base, and other in- 
stallations. The Army projects have been AN-4 
(low altitude bombsights), AC-36 (CRAB 
guided bombsight), and AC-121 (rocket 
sights). In the case of both Services, a good 
deal of work, both concrete and of an advisory 
nature, has been done under no official project 
whatsoever. Thus, in connection with projects 
which were related to those for which control 
numbers had been assigned to us, the writer 
was requested by BuOrd of Navy to advise 
directly on certain projects placed with Navy 
contractors. Instances include Specialties, Inc., 
at Syosset, New York, and Polaroid Corpora- 
tion in Cambridge, Massachusetts. 

CONTRACTORS 

First, with regard at least to groups under 
contract to NDRC Section 7.2, it is well known 
that in general all organized technical pursuits 
under NDRC direction are set up through the 
facilities of such contractors. The present 
writer has had most to do with the contract 
(OEMsr-330) at The Franklin Institute in 
Philadelphia, where a major portion of the 
section’s airborne fire control developments 
have been conducted. The research group here 
has been built, with considerable assistance 
and molding by the section, from a nucleus of 
four engineers to a staff of several score tech- 
nical personnel, augmented somewhat by the 
staffs and facilities of several subcontractors. 
Laboratory, office, and drafting space have 
been prepared and occupied gradually as 
needed. Sharing such facilities as experimen- 
tal, computing, drafting and model shop, the 
project staff blossomed horizontally into groups 
devoted to torpedoing, bombing, gunnery, rock- 
etry and integrated equipments. The heads of 
these groups reported to the coordinator for 


rONFIDENTIAL 


6 


PREFATORY COMMENTS 


the contractor, who has been R. H. McClarren. 
Guidance in technical policy and project plan- 
ning has been given by the section staff through 
the agency of a steering committee which was 
formed rather early in the history of this con- 
tract. McClarren served this committee as non- 
voting secretary, and the remainder of the 
members was constituted of S. H. Caldwell 
(ex officio), A. L. Ruiz, H. C. Wolfe, E. G. 
Pickels, and until recently J. B. Russell, with 
the present writer as chairman. Aside from 
his existence in the latter capacity, however, 
the writer was also held responsible for a 
specific number of developmental projects as 
such. Although in connection with such projects 
he owes much to specific personnel at The 
Franklin Institute, mention of the numerous 
men thus concerned will be reserved for the 
more detailed and relevant portions of the 
report. 

In connection with a contract undertaken 
for Section 7.2 by the Stanolind Corporation 
in Tulsa, Oklahoma, the writer was given sur- 
veillance of the development of a mechanical 
pursuit-collision course plotter, proposed by 
M. Alkan of Specialties, Inc., for assistance in 
the design of a Navy dive bombsight. Prin- 
cipal contact at Stanolind was with D. Sil- 
verman. 

Through a contract with Columbia Univer- 
sity, at the Marcellus Hartley Laboratory, the 
section conducted electronic projects under 
J. A. Balmford and J. R. Ragazzini there. As 
was the intent, such work largely served and 
supplemented that in progress within the 
larger group at The Franklin Institute, and 
covered certain servomechanism developments 
as well as simulative endeavors. In addition, 
however, electronic simulative studies were 
conducted on steered projectiles for projects 
being pursued by Section 7.2 in collaboration 
with Division 5. This branch of the contract 
was taken under the direct sponsorship of 
Division 5 in the summer of 1945 and was 
placed within a contract with Specialties, Inc. 
The reader is referred to Chapters 4 and 8. 

Under contract to the section. The Bristol 
Co. has also contributed to researches at The 
Franklin Institute, and through the services 
of C. A. Mabey, A. W. Jacobson, and G. M. 


Thynell has aided in the preparation of special 
mechanical linkages for components of com- 
puting sights under development. 

The writer has had considerably less to do 
with the others of the section’s contracts, 
which include those at General Electric on 
B-29 computers, at Northwestern University 
on assessment methods, at University of Texas 
on gunnery evaluation, and at Jam Handy 
Corporation on vector sights, etc. 

With several of the other contractors of 
Division 7, highly beneficial cooperation has 
been indulged in on projects of mutual interest. 
Through the provision, by Section 7.3 for ex- 
ample, of certain facilities of Lawrance Aero- 
nautical Corporation, Linden, New Jersey, the 
design of pneumatic components has been 
greatly furthered on our Navy projects. Fa- 
cilities also of Eastman Laboratories in Roch- 
ester have similarly been made available, under 
the stewardship and incentive of E. J. Poitras 
and J. F. Taplin of Section 7.3. An earlier ex- 
ample of such collaborative effort on pneumatic 
instrumentation, which resulted ultimately in 
bombsight Mark 23, involved the McMath- 
Hulburt Observatory at Lake Angelus, Michi- 
gan. 

Far too numerous for exhaustive tabulation 
are the contractors of NDRC divisions other 
than Division 7. However, the Radiation Lab- 
oratory at the Massachusetts Institute of Tech- 
nology [MIT] must be mentioned as being in- 
volved in several connections, in connection 
particularly with the provision of automatic 
plane-to-plane and plane-to-ground ranging 
equipment. Tangible help on a variety of prob- 
lems has been received from many of the staff 
there. We mention also the California Institute 
of Technology, under Division 3, in connection 
with rockets, where C. C. Lauritsen, W. A. 
Fowler, C. G. Anderson, and others have ren- 
dered assistance. With that portion of the Bu- 
reau of Standards under Division 4, we have 
dealt profitably with W. B. McLean on toss- 
bombing studies. The contractors of Division 5 
have been concerned, both through interdivi- 
sional collaborative arrangement, and by the 
writer directly as consultant to that division; 
these dealings are reported jointly since separa- 
tion is not feasible. Such contractors include: 


i 


(DXFTDKXTIAj 


FORM AND REFERENCES 


7 


Gulf Research and Development Co. in Pitts- 
burgh, where we have cooperated on guided 
bomb controls with E. A. Eckhardt, R. D. 
Wyckoff, and J. P. Molnar among others ; RCA 
Laboratories (Zworykin) at Princeton in con- 
nection with television for homing bombs ; 
Douglas Aircraft in Santa Monica, where 
W. B. Klemperer, E. W. Wheaton, and many 
others were extensively cultivated with regard 
to the ROKH projectile in its several phases; 
L. N. Schwien Engineering Co. in Los Angeles, 
with L. N. Schwien and H. A. VanDyke on 
stabilization and other control techniques; and 
Bendix Pacific Division in Hollywood, with 
W. S. Leitch on radio links. 

Special mention must be made of the Applied 
Mathematics Group at Columbia, under con- 
tract to the Applied Mathematics Panel [AMP] 
of NDRC. Incalculable aid has been received 
from this group, with which we have worked 
quite closely on several fire-control projects. 
The notables include S. MacLane (Director), 
H. Whitney, H. Pollard (the two latter having 
had local office headquarters in the writer's 
office in Cambridge), I. Kaplansky, L. C. Hutch- 
inson, and D. P. Ling. Particular operations 
thus valiantly served were rocket sights, toss- 
bombing equipment, and pilot’s universal sight- 
ing systems; relating to Service projects 
NO-216 and NO-265. Certain other groups un- 
der AMP were similarly useful, though as it 
happened in less major connections. 

In connection with researches on controls 
for guided bombs the differential analyzer at 
MIT has been made available for an extensive 
study of controlled trajectories in two and 
three dimensions. Engaged at first through the 
contractual machinery of Division 7, and later 
through that of Division 5, this facility made 
possible an articulate numerical treatment of 
a problem which could not otherwise have been 
handled without years of computation by a 
large staff expertly led at every point. The staff 
of this analyzer, as of the Center of Analysis 
itself at MIT, contributed mightily in this work. 

Wherever, in the present report, the writer 
refers to “our laboratories,” this impropriety 


should be interpreted as a manner of speaking, 
which has arisen out of habit, rather than in 
a precisely literal sense. The laboratories of 
The Franklin Institute contract are most likely 
thus to be connoted, and perhaps, even those 
at Columbia. The possessive pronoun is a con- 
sequence of the part the section has played in 
building up such facilities and in organizing 
the research which has been pursued. 

FORM AND REFERENCES 

The monographic form for this report, with 
its set of sub-monographs on the separate tech- 
niques and fields of endeavor, was chosen by 
the writer out of his personal preference for a 
unified literary entity. It should be possible, 
however, to separate, discard, or reassemble 
the various parts hereof in whatever manner 
appears desirable to suit a larger need. No de- 
tails are here bodily reproduced which are 
available elsewhere, although brief outlines of 
such fuller material may be categorically in- 
cluded in reference to related topics. 

Certain of the writer’s own contributions, 
in either theoretical branches or concrete mech- 
anism, may here be found discussed with an ap- 
parently unwarranted emphasis. In such cases 
the reason for such treatment is that docu- 
mentation of these items is not likely to be 
found at other sources, or may there be but 
baldly referred to. 

A serious attempt is made to give proper 
credit and to make equitable references to 
original enunciations and reductions to prac- 
tice. If this is imperfectly achieved, it is with- 
out malice. Contractor’s reports are referred 
to liberally, but more thorough search of these 
is indicated for the details of any given aspect 
which may later become significant. Writings 
of such collaborating mathematicians as H. 
Whitney and H. Pollard (of AMG-C) are volu- 
minous and frequently contain definitive docu- 
mentation of methods and components which 
we have been too eager to build and try, in 
contrast to the compulsions of our manifest 
duty to disseminate. 


LONFTOENTIAL*; ^ 



Chapter 1 


GENERAL THEORY OF AIMING PROCESSES 


SCOPE AND LIMITATIONS 

T O THE PRESENT CHAPTER we have relegated 
as much as possible of the general and theo- 
retical background which is relevant to the 
rest of the report. There is introduced here 
not only an account of the mathematical scaf- 
folding which is typically to be employed, but 
also a number of the physical and dynamical 
principles on which the numerous aiming de- 
vices rest. The presentation is elementary, as 
indeed are the principles themselves, but it 
is considered that a service will hereby be 
afforded in characterizing both the mode of 
approach to problems and the sort of descrip- 
tion and explanation which is employed 
throughout. 

The various branches of fire control are based 
to a remarkable degree on a common technical 
foundation. Although this is not surprising on 
the face of it, nevertheless it is found impres- 
sive to the worker in tangible apparatus as 
his attention shifts from one field to another, 
and this is true no matter how extensive his 
experience and however sophisticated his 
philosophy. The realm of statistics and proba- 
bility is not strictly included in these remarks, 
for it is of broader significance yet. This realm, 
although inseparable from the theory and in- 
strumental techniques of the subject of this 
report and serving it in all phases when ap- 
plied in the economy of effort and the concen- 
tration of effectiveness, is entered into here 
only to a minor degree. Being treated far 
more completely and competently elsewhere, 
and applying more indispensably, for example, 
in the larger senses of assessment, the methods 
and accomplishments of statistics are substan- 
tially omitted from these pages. Thus, even 
in the development of automatic mechanism as 
such, what is included must be considered only 
a factor in the whole assemblage ; but it is this 
factor on which we have specialized, and such 
emphasis is properly descriptive of the activity 
to be documented. 


Another reason for the inclusion of the pres- 
ent chapter is to record, in close association 
with the individual treatments of apparatus 
and of its development, a self-consistent, albeit 
somewhat diluted, compendium of definitions 
for the several terms and phrases which are 
peculiar to this field and to which allusion is 
frequently made. This is considered advisable 
owing to the rather large and widespread dis- 
parity which is evident among the current 
users of such nomenclature. It will be apparent 
to the reader that certain departures are herein 
made from usages and conventions which are 
orthodox in this field. In such cases the diver- 
gence is commonly for the purposes of in- 
creased generality, to which end the writer 
perpetually strives ; and an attempt is made to 
identify such innovations, locally, with the 
more familiar and restricted concepts. 

12 the position vector 

Among the symbolic languages which are 
available to the dealer in fire controls, that of 
the free vector is one of the most direct and 
articulate. We build here the structure of such 
vectors which describes a system of points in 
motion in a medium. While falling short of the 
more general rigid-body dynamics, such sys- 
tems are everlastingly serviceable for the em- 
bodiment of a great fraction of the funda- 
mentals hereto relevant. 

Consider first a point which is stationary in 
a given medium, the latter being unaccelerated 
in space and for the present purposes uniform. 
This point, which may be called a, is typical of 
and may identify the medium. It may have 
been quite arbitrarily chosen. 

A second point, moving in or with respect 
to this medium, may be symbolically identified 
as h. The position of the point in the medium, 
or with respect to point a, is to be described 
completely by the vector Ra?,, which may be 
thought of alternatively as the ‘‘directed 


Gi 


confidkntta; 


9 


10 


GENERAL THEORY OF AIMING PROCESSES 


range’’ from point a to point in that order. 
The vector so expressed denotes both distance 
and direction, in accord with the normal capa- 
bility of vectors. When this vector is constant, 


b 



Figure 1, Standard iiosition vector. 

the second point is stationary with respect to 
the first point, and hence in the medium there- 
by identified. When this vector is variable, 
being for example a function of time, then if 
its origin is located in point a, the tip of the 
vector traces out the space-path of the moving 
point b in the medium. 

When point b approaches point a, the vector 
Rah approaches R„a, which is the null vector 
although not necessarily the number zero. The 
scalar or inner product of Rah with itself, that 
is Rah * Rahy gives the square of the absolute 
scalar magnitude of the vector Ra?,, and in this 
case is also the square of the undirected dis- 
tance or true range of point b from point a. 
Of the many notations which are current for 
the scalar magnitude itself, we mention 
|R„ 7 , |. We shall denote this quantity here by 
the scalar symbol Rah, as in 

R~ab = Ra6 • Ra6 • (1) 

It is intended that this quantity contain, or 
carry with it, the physical dimensions, if any, 
of the vector Ra^. The quantity Rah, then, is the 
distance (in feet, say) from the point a to the 
point b. 


Consider next the vector kRah, defined as the 
position vector, with respect to point a, of a 
point collinear with a and b, and which is k 
times as far from a as 6 is. Its scalar magni- 
tude is certainly kRah- The scalar multiplier k 
may be purely numerical, in which case it pro- 
duces merely a stretched version of the origi- 
nal vector, or it may have physical dimensions 
and thus alter the character of the original 
vector. If we arrange that k = R~aU then the 
so-called unit vector, having a scalar magni- 
tude of unity, is produced. This unit vector in- 
dicates only the direction of the point b from 
the point a and may be given the symbol I’a?,; 
thus : 

Tab “ Rab Rob Of Rab “ Rah ^ab • (2) 

The unit vector is undefined when the scalar 
Rah is zero. It is further evident that the unit 
vector does not have, in this sense at least, any 
dimensions. 

If the position of point b with respect to 



Figure 2. L^nit vector and its multiples. 

point a depends in either a preassigned or a 
determinable way on time, then the vector R„b 
is said to be a function of time. That is 

Rab = Rab(0. 

In many circumstances, particularly in signifi- 




ANGULAR RATES 


11 


cant physical cases, this variable vector will be 
differentiable. For example, if it is considered 
that Rab is the triple of three rectangular co- 
ordinates, then in such circumstances these co- 
ordinates are also differentiable in the scalar 
sense. On this assumption we define the vector 


as the vector velocity of the point b with re- 
spect to the point a, or in the medium thereby 
identified. This vector, as a function of time. 





a 

Figure 3. The vector derivative. 


is parallel to the tangent to the space-path of 
point b in this medium and in length is pro- 
portional to the velocity of b along this path, 
both being instantaneously evaluated at the 
time t. The scalar value or magnitude of ¥«& 
is similarly defined as | Va& | or Vab, where 

Fl, = V.6-V.,, (4) 

and the unit vector, giving purely the direction 


of motion of the point b in the medium and 
with respect to a, is symbolized by v^b, where 

^ ab ~ Fa6 ^ ab • (5) 

Individual constancy of the various quan- 
tities in equation (5) is significant as follows. 
If the unit vector Vab is constant, motion of the 
point b in the medium is rectilinear; if the 
scalar Vab is constant, then this motion involves 
an unchanging speed along the path ; and 
finally the constancy of the vector velocity Yab, 
which implies both the above, means unacceler- 
ated motion of the point b in the medium iden- 
tified by the point a. 

» 3 ANGULAR RATES 

Still with regard to the two points a and b^ 
and to the fundamental vector Rab, we may 
show how rates of rotation enter the scheme 
as the time derivatives of unit vectors. First 
differentiate the second expression given above 
as (2) for the vector Rab, obtaining thus 

Rab ~ Y ab ~ Rab l*ab “1“ Rab ^ab • (6)' 

Noting that I’ab is in magnitude proportional 
to the angular rate of point b about point a, 
and is normal to Rab and coplanar with Rab 
and Vob, and noting also that Rab (which is dif- 
ferent from Fab) is merely the range rate be- 
tween a and b, we can identify the terms on 
the right-hand side of the vector equation (6) 
as the components of Yab which are normal to 
and along the direction Tab. 

Pursuing further the derivative Vab of the 
unit vector as a measure of rotation in space, 
we may construct an even more articulate such 
vector by taking the outer or vector product 
of Tab into Tab, which may be symbolized as 
fob X rab- Thus we define 

^ab “ I’ab X Tab , (7) 

and it will be seen that this vector is a measure 
of the time rate of angular rotation in space 
of the point b about a which is normal to the 
plane of rotation and which is directed in the 
right-handed, or screw-thread, sense. 

When the vector velocity of the point b in 
the medium is invariant, that is when Rab = 


12 


GENERAL THEORY OF AIMING PROCESSES 


\ab is constant, then the area of the parallelo- 
gram formed, in the invariant plane of rela- 
tive motion, by the vectors Rab and Yab is evi- 
dently constant. Thus by definition of the vec- 
tor product we have, in such a case, 

Rab X Yab = Constant. 

But now Rab = Rab Yaby and by performing vector 
multiplication on both sides of (6) with this 
latter product we find also, referring to (7), 

Rib [i*ab X fab] = Rib Qab = Constant. (8) 

This relation is seen to embody a vectorial ex- 
pression of the well-known invariant (range- 
squared into angular rate) for unaccelerated 
straight line courses. 

SEVERAL POSITION VECTORS 

Keeping the initial point a as identifying 
symbol for the single medium, consider now 
two points, b and c, having general motion 
therein. With the same convention for a rela- 



Figure 4. Relative position and relative velocity as 
vectors. 

five position vector, we can express the posi- 
tion of the point c in the medium as 

Rac = Rab + Rbc , (9) 

in recognition of the triangle formed in the 
medium by the three points a, b, and c. The 
notation employed provides a convenient cri- 
terion for cancellation of indices on summing. 
Note that scalar multiplication, of each of 

V 


the two sides of (9) into themselves, yields the 
familiar law of cosines. 

Differentiation of (9), giving 

Yac = Vob + Vbc , (10) 

shows that the vector velocities, one relative 
and two with respect to the medium, add vec- 
torially and form a closed figure as do the 
position vectors themselves. A similar rela- 
tion holds no matter how many points are in- 

INITIAL POSITION OF 
VEHICLE AND PROJECTILE 



INITIAL 

TARGET 

POSITION 


Figure 5. Hitting criterion as vector sum. 

volved and no matter how many derivatives 
are taken. 

If point c is moving in an arbitrary manner 
in the medium, and if the instantaneous mo- 
tion of point b, with respect to the medium, is 
directly toward point c, then 

Vab = A'Rbc (11) 

where k is some positive scalar quantity. But 
since we may write 

I ab Tab — kRbc I*bc 

it follows that 

k = Rbj Vab 

and 

Vab=rba, (12) 

since the scalar and the directional equations 



REMARK ON ANGLE 


13 


must be satisfied. The latter equation may 
hold either instantaneously or identically and 
forms the definition of a pursuit course with 
reference to a path in the medium. Where h 
is a point in a body, of which some axis may 
be pointed at c, the pursuit course may be dif- 
ferently defined. We shall prefer here, how- 
ever, to use the term as characterized by (12). 
Note that the derived criteria 

\ab X Rfcc = 0 , 

and 

Vafe X Fftc = 0 (13) 

may describe either a pursuit course, in the 
above sense, or its negative : the one point mov- 
ing aivay from the other. 

When the two points h and c are moving 
uniformly in the medium, so that Vcb and Voc 
and hence also are constant, a simple cri- 
terion may be exhibited for the coming to- 
gether of these two points. Such coming to- 
gether is of course refiected in the vanishing 
of both the relative position vector R&c and of 
its scalar magnitude and may be a desired 
event if, say, & is a bullet and c its target. Since 
now Vbc is a constant, and since consequently 

RfccCO = R6c(0) + (14) 

which must vanish at some value of in the 
future for example, we have, somewhat as 
before, 

Tfec + Vftc = 0 (15) 

as the criterion for the collision course in the 
sense indicated. Since absolute motion has not 
latterly been employed, in the medium that is, 
this criterion implies collision even when 
Yab and Voc are variable, provided only that their 
difference V^c is constant. The oppositely point- 
ing unit vectors of (15) insure the ‘"closing of 
the range.” A hypothetical collision in the past, 
with the range opening, is of little comfort in 
those forms of fire control which require a co- 
incidence; such a “recessive” collision course, 
however, may be quite useful in some aiming 
processes to be described. 

A type of generalized collision course is de- 
fined by the simple criterion 

he = 0, (16) 

which implies equation (15) when the mo- 


tions are uniform. In general, however, 
neither condition insures a collision since the 
range may increase or approach a limit. Equa- 
tion (16) is the vectorial version of the con- 
stant true hearing criterion which is familiar 
in homing operations. Dynamical relationships 
which subside to this condition, or which are 
able to approximate it identically, are of ex- 
treme interest in such operations. 

Of course the necessary and sufficient con- 
dition (we repeat) for ultimate coincidence of 
points h and c is that, at some time, 0, 

however this is brought about. 

When equation (16) is taken together with 
the constant-range criterion R^c — 0, then they 
together imply R^c == 0. Points h and c are then 
translating similarly in the medium or are 
“flying formation” in a very ideal sense. 


REMARK ON ANGLE 

Although there appear to be several natural 
forms of notation for angular rates, such as 
that shown above, which come out of the 
straightforward vector constructions, there 
seems to be no supremely convenient notation 
for the angle between two vectors. 

The vector product is proportional to the 
sine of such an angle, as well as to the product 
of the magnitudes of the vectors themselves, 
and shows the sense in which the angle is swept 
out. If the vectors are first normalized, or 
reduced to unit vectors, and the vector product 
then evaluated, the resulting vector shows the 
sine of the angle, the plane which contains it, 
and the sense of rotation. 

Further as to unit vectors, the difference be- 
tween two of them is demonstrative of the an- 
gle (and its sense) between the two directions 
thereby indicated. The scalar magnitude of 
this vector difference is twice the sine of half 
the angle. 

A further measure of the angle, in terms of 
vector concepts, was considered.^ Referring to 
any two vectors, a vectorial measure of the tan- 
gent of the angle between them, properly 
signed, is given by the ratio of their vector 
product to their scalar product. The resulting 


®In conversation with A. L. Ruiz. 




ONFIDENTIAL 


7 


14 


GENERAL THEORY OF AIMING PROCESSES 


vector is normal to the plane in which the an- 
gle may occur. With a simple notation worked 
out, this measure of angle should be extremely 
useful, owing partly to its compactness and to 
the remarkable usefulness of the tangent in 
many classes of problems. 


16 A PROJECTILE 

Retaining the terminology of vectors, we 
shall next discuss a problem in the aiming of a 
projectile, and while giving the problem a cer- 
tain generality we shall assume certain ideal 
circumstances which are not always satisfac- 
torily descriptive of real conditions. Frequent- 
ly, however, under real circumstances, trans- 
formations may be made in a problem so that 
an equivalent problem in the more idealized 
state is obtained; and even more commonly 
the simpler but less realistic study has high 
educational value, and may provide a starting 
point from which to expand toward a more 
complex reality. 

Following a presentation of the rationalized 
problem, with its significance properly qualified 
as above, we shall discuss several special cases, 
having fewer space dimensions and involving 
more specialized physical phenomena, as being 
introductory to some of the aiming stratagems 
which are described elsewhere in this report. 

In a medium as above, identified by the point 
a (not shown in Figure 5), let there be a 
vehicle b, that is to say which is represented by 
the point b, and an enemy target c. Let it be re- 
quired to launch a projectile from the vehicle 
so as to coincide at some time with the target ; 
and let the projectile be identified by point d. 
Assume first that the target c is moving uni- 
formly in the medium, which may be the air 
mass. Assume further that the projectile, when 
launched or released or projected or fired, pro- 
ceeds initially in the same direction in the me- 
dium as the vehicle at that instant is proceed- 
ing, except k times as fast. Its initial velocity, 
with respect to the vehicle, is then (/c — 1) times 
the velocity of the latter. Suppose also that, al- 
though the medium offers no net resistance to 
the projectile, gravity acts upon it in a normal 
manner. With time measured from an origin at 


the instance of firing, the position of the pro- 
jectile in the medium is 

Rad(0 = Ra6(0) + t\ab(0) 

+ (/c-l)Wa6(0) (17) 

where the vector A^ is the acceleration of grav- 
ity, acting downward. This vector may be 
considered invariant, and may further be writ- 
ten gr^ where g is the scalar acceleration of 
gravity, and r^ is a unit vector, downward 
pointing. 

The target position, however, is 

Rac(0 = Rac(O) + t\ac{0), (18) 

to which, of course, acceleration terms may be 
added in the more general case of nonuniform 
motion. Equating (17) and (18) for a hit, and 
letting the value of t which satisfies the result- 
ing equation be tf, the time of flight, we have 

RfecCO) = — tfVbciO) + {k — l)tfY ab{0) . {19) 

The relative position vector Rbc(O) is the vec- 
torial present range, while Vbc(O) is the pres- 
ent relative velocity of the target. We note 
that if these quantities are continuously avail- 
able, together with the vehicle velocity Yab and 
the “down” direction r^, then the solution to 
the aiming problem is given completely by 
equation (19). It is unnecessary to know the 
scalar tf since this equation determines Vo&, for 
example, in terms of the other three vectors, 
and a mechanism could be built to steer the 
vehicle along the vector Y'ab which would make 
the equation hold, for whatever tf were thus 
required. The magnitude of the latter variable 
would be an outcome, incidentally, of this auto- 
matic computation. 

Although vectorial mechanism, in three di- 
mensions, would be thoroughly practical for 
computation, the commoner types of mech- 
anism deal in scalars and in fewer dimensions 
at a time. 

For the moment let us omit the consideration 
of gravity, and restrict attention to a particu- 
larly simple situation in two space dimensions 
(Figure 6). The relative position vector R^c be- 
comes a line segment in the plane connecting 
the vehicle and the target. The velocity vectors 
of vehicle and target may then be attached at 
the appropriate ends of this line segment. It 


A PROJECTILE 


IS 


is evident that if the vehicle velocity Yab lies 
along the relative position vector R^c, a pur- 
suit course is signified. If, on the other hand, 
the projections, normal to the position vector 
Rftc of the two velocities Yab and Yac are equal, 



and if further these are constant, then we have 
one condition for a collision course: in the re- 
stricted sense. The other condition is a uniform 
decrease of the scalar range R^c, which cri- 
terion may also be expressed in terms of the 
projections of the two vector velocities along 
the connecting line segment or vector. Simi- 
larly, a collision course for a projectile is de- 
scribable by replacing the vehicle velocity by 
its appropriate multiple 

Yad = kYab = Yab + ~ l)Va6 . 

Referring to the scalar magnitudes only of 
the figure last indicated, we may reiterate, as 
follows, the several remarks already made. If 
the “lead” angle A, as shown in this figure, 
is zero, the pursuit course is in effect. If the 
lead A is such that 

Vab sin X = Vac sin a, (20) 

then a collision course results. Further, if 
Vad sin X = (Vab + Vbd) sin X = Vac sin a , (21) 

a projectile launched under these conditions 
will hit the target. 


A general fact which relates to the circum- 
stances here pictured is contained in the 
identity (cf. Figure 6) 

& = VacRrc^ sin a — VabRVc^ sin X . (22) 

Thus by relation (21) it is seen that a criterion 
for hitting is given by 

sin X = RbcVbl & , (23) 

which requires no measurement of the target 
velocity. It should be noted that all these scalar 
expressions may be given as concisely, if some- 
what less familiarly, in vector notation. 

To return to equations (20) and (21), we 
shall illustrate methods for finding aiming 
criteria without explicit use either of the tar- 
get velocity or of the range. We restrict our- 
selves, naturally, to the assumptions already 
enforced. Suppose that a collision course be 
momentarily obtained, for example, through 
use of the criterion 

& = 0. (24) 

Under these circumstances, as indicated both 
by equations (20) and (22), we know that 

Vac sin a — Vab sin X* , (25) 

where A* indicates the (measurable) lead on 
a collision approach. Thus from equation (21) 
we find that the angle A for a hit is given 
in terms of quantities locally available, by 

sin X = (I + Val VbdT^ sin X* . (26) 

The flight path of the vehicle need only be ro- 
tated through the angle A* — A toward the tar- 
get, to pass from a collision course to a firing 
position. 

Instead of the initial collision course, suppose 
that a pursuit course is initially employed. 
Since then A = 0, we have 

&* = VacRbl sin a, (27) 

where a* is the angular rate in space of the 
line to the target during the initial pursuit ap- 
proach. Then assuming the range does not 
change substantially during the transition, we 
alter the course so that, by equations (22), 
(23), and (27) 

& = &* — VabVll & , 

or so that 

(i- = (1 + (28) 

Again a firing criterion, in terms of an initial 


^OTIDENTIAI. I 


16 


GENERAL THEORY OF AIMING PROCESSES 


maneuver, is made available without employ- 
ment either of the target velocity or of the 
range. The evident similarity in form between 
equations ( 26 ) and ( 28 ) is rather remarkable. 
With regard to the latter criterion it should be 
noted that the inevitable change in range dur- 
ing the transition may be roughly approxi- 
mated, and that this must be done if high ac- 
curacy is required. In the writer’s opinion, 
both of these fundamental methods for kine- 
matic lead computing are worthy of note, for 
example when the range becomes difficult to 
compute, and it seems to him that there may 
exist practical composite methods which lie 
somewhat between the two. The principal pur- 
pose, however, of their present introduction is 
illustrative rather than developmental. Along 
practical lines, the stability of the aiming 
process, in each case, would require much 
closer attention than has here been indicated. 

SPACE-TIME GEOMETRY 

We wish here to exemplify, in connection 
with some of the aiming criteria discussed 
above, a method of visualization, or rather of 
symbolic representation, which may always be 
substituted for the vectorial one, and which 
in many cases, particularly to the geometrically 
inclined thinker, may be preferable thereto. 

Again suppose that we are dealing with two 
space dimensions, but that in addition time is 
taken to be represented as a dimension normal 
to the plane of ‘‘space.” In the resulting three- 
dimensional volume then, a point represents 
an event, and the coincidence or intersection of 
two paths generated by such points corre- 
sponds to a simultaneous coincidence of real 
points. This is in contrast to the properties of 
vectors in the normal portrayal where time is 
not a dimension. 

In the adjacent figure, the projection of all 
points on to the space-plane reduces the whole 
affair to the conceptual scheme which has been 
employed above. For the rest, the interpreta- 
tion is remarkably simple, although admittedly 
this is true, in a conceptual sense, only because 
we are temporarily restricted to two dimen- 
sions of space. It is evident, for example, that 
unaccelerated motion of a point resu-lts in a 


straight line in the space-time volume shown; 
a stationary point forming a line parallel to 
the time axis, and an infinitely fast point lying 
altogether in one space-plane. It is further seen 
that the velocity of any point is given by the 
cotangent of the angle between the space-plane 



and the tangent line drawn at the given point 
to the three-dimensional path traced out by this 
point. 

Consider two points in motion in a medium 
which is stationary in the space-plane, the 
origin of the latter being, for example, the 
identifying point of the medium in the manner 
already explained. At a particular time, the 
positions of these points in the particular space- 
plane corresponding to this time may be taken 
as initial positions for the two points. Assum- 
ing then that the two points have a given 
constant velocity and are to be unaccelerated 
in the future, we see that their possible space- 
time paths lie along the elements of cones 
which have axes parallel to the time axis. The 
tangent of half the vertex angle of each cone 
corresponds directly to the preassigned veloc- 
ity of each point. If for one point a given 
direction in space be chosen, and hence just 
one element of its cone of motion is singled 
out, then the one element of the other cone 


t ^NFIDKyilATvi 


SYNCHRONOUS OPERATIONS 


17 


which intersects that of the first cone is like- 
wise singled out, and consequently the direction 
of motion for the second point is determined 
which will result in collision. Such a solution, 
which may readily be reduced to straight- 
forward mechanical form, will apply whether 
it is desired that the vehicle itself collide, or 
that an aimed projectile coincide at some fu- 
ture point with the target. 

The generalizations of the above conceptual 
scheme to include such effects as that of grav- 
ity, accelerated motions, and so on, may well 
be imagined. Mathematically at least, there is 
no need to perpetuate the restriction to two 
space dimensions, although indeed only the 
sections and projections of the resulting hyper- 
cones can conveniently be visualized. The pres- 
ent writer has found the space-time mode of 
thinking to be extremely useful, even when 
limited to special cases, for the tangible illus- 
tration of the more drastically complex situa- 
tions of typical and practical problems. 

18 SYNCHRONOUS OPERATIONS 

As an example of the useful employment of 
an operation of the synchronizing variety, so- 
called, suppose that it is required that the ab- 
solute velocity vector of a target be accurately 
determined from a moving vehicle, and that 
only the direction and distance to the target, 
that is to say its relative position, are available 
to some approximation. Note first that the 
relative position vector at any time t may be 
expressed as follows 

R6c( 0 = RfccCO) + f \bc{t)dt; 

Jo 

or further as 

Rbcit) = R6c( 0) + r [yacit) - \amdt . (29) 

Jo 

If now Vo6 be continuously measured, as a local 
variable, and if the relative position Rbc(O) of 
the target be once determined at a given in- 
stant, then by generating an artificial version 
Vac(0 of target velocity, an artificial version 
of the relative position may be produced as 

= RicCO) [V„(<) - V„»(t)]*. (30) 

If adjustment of Voc(0 is made in continuous 
dependence on the observed vector error 


Rbc(0 — Rbc(t) and is made so as to reduce 
the latter stably and accurately to small mag- 
nitude, and if such stability and accuracy is 
continuously maintained, the artificially gen- 
erated Yacit) can be a faithful version of the 
true target velocity Vac(t) • Errors in the initial 
target position Rbc(O) are integrated out in this 
process, but errors in the determination of 
Va&(0 contribute to errors in the target speed 
in direct proportion to the numerical speed 
advantage. 

In tracing out the causal sequence involved 
here, we note that the operator (whether hu- 
man or automatic) observes the difference be- 
tween the generated vector R^c and the vector 
Rftc describing the relative target position, and 
on the basis of this difference manipulates the 
artificial target-speed vector Voc- Through the 
agency of apparatus which mechanizes equa- 
tion (30), this artificial target s^ed influences 
the generated position vector R^c, which in 
turn affects the observed difference, and so on 
in continuous fashion around the loop. If the 
ope£ator manipulates the vector Rftc(O) as well 
as Vac, this may result in a closer following of 
Rftc by Rftc, or in “better tracking,” but such 
manipulation if irregularly and continually 
employed result^ in serious errors in the ap- 
proximation of Voc to Vac. Such combined op- 
eration is a vectorial generalization of “aided 
tracking.” If, however, the two adjustments 
are appropriately interconnected, easier and 
better tracking as well as faster subsidence to 
an accurate version of the target speed will 
result. Thus notice that for a given error in 
the latter, in Vac— Vac that is, ;^e requisite ad- 
justment of Rbc(O) to make R^c momentarily 
equal to R^c increases in proportion to the 
time. Hence if each adjustment in Rbc(O) is ac- 
companied by ^simultaneous and proportion- 
ate change in Voc, where this change is also 
proportional inversely to the time intervening 
since the last previous adjustment, then sub- 
sequent readjustment need only deal with 
errors of higher order. 

We note that this whole process can be gen- 
eralized as far as may be desired. In equation 
(30) , Vac niay be replaced by 

YaciO) + [ Ajt)dt, 

J 0 



18 


GENERAL THEORY OF AIMING PROCESSES 


where Aac is the artificial target acceleration 
vector (in space). Three adjustables now re- 
place the above two, and these may be simi- 
larly ii^erconn^ted, with the intercoupling be- 
;^een Aac and Voc(O) resembling that between 
Vac and Rftc(O). This procedure may improve 
the tracking and the representation of target 
speed, and may furthermore provide a “syn- 
chronous” measure of target acceleration for 
higher order solution to fire-control problems. 

MORE ON THE APPROACH 

We have discussed above, both in vectorial 
and in scalar form, the properties and criteria 
pertaining to pursuit and collision courses for 
the approach by a vehicle to a target. Among 
the infinite variety of such modes of approach, 
of which these are but special cases, we shall 
outline one here which may begin as a course 
of pursuit and then subside with arbitrary 
rapidity toward a course of collision. In this 
process we shall show means whereby such 
an approach may be controlled. 

Suppose initially, in the plane of Figure 6, 
for example, that the vehicle b is in direct pur- 
suit of the target c, or that 


referred to as proportional navigation. The 
technique will reappear at several points 
within the present report. 

In order simply to illustrate the consequences 
which follow the imposition for this criterion 
of approach, the following assumptions shall 
be made: We assume the scalar speeds of vehi- 
cle and target, Vah and Vac, are constant, and 
further that the target has motion only nor- 
mal to the line connecting it with the vehicle. 
We assume also that the lead angle A is suf- 
ficiently small that the angle is an adequate 
approximation for its sine, and so that the rate 
of change of the range is contributed to only 
by the vehicle speed. 

It is evident, under the above assumptions, 
and by reference to Figure 6, that for a colli- 
sion course 

X = r = (33) 

where the new symbol A identifies the lead for 
a collision course. Equation (22), under the 
same assumptions, becomes 

Rhc a = Vac — Fa6X (34) 

while also 

Rbc ~ V ab 


X(0) = 0. 


( 31 ) Now combining (32), (33), and (34) we find 


We propose subsequently to change the direc- 
tion of motion of the vehicle, measured by the 
angular sum o- + A, at a rate proportional to 
that at which the direction to the target, 
measured by the angle o- itself, is changing. We 
propose further to make the changes in the 
direction of motion of the vehicle occur k times 
as fast as those in the direction of motion of 
the target, or to make 

X + (7 — O' (0) = k[a — or (0) ] . 

The derivative of this criterion provides a more 
succinct description: 

\ = {k- 1)&. (32) 

Thus a paraphrased criterion is to make the 
rate of change of the lead angle A:— 1 times as 
large as the rate of change of the absolute di- 
rection of the target. This mode of approach, 
for which it is evident that several other sym- 
bolic descriptions may be given, is sometimes 


dX 

A — A rihc 


0 ; 


and upon integration 

,, _ /Rkc (1)^-1 


(35) 

(36) 


which means that the lead A approaches the 
value A for a collison course in proportion to 
the (A; — 1) power of the fractional closure of 
the range. It is evident that for large values 
of the ratio k the collision condition is attained 
very rapidly. For k = 2, notice that A, o-, and 
consequently \ -\- a- are approximately con- 
stant. This implies a constant rate of turn of 
the vehicle and corresponds to the so-called 
circular-interception approach. 

We repeat that the above analysis is ap- 
proximate, but within reasonable limits it 
shows substantially the same phenomena as 
does the considerably more difficult exact treat- 


roXFlDTTSlTXlZ 

... , , m 


FEEDBACK IN GENERAL 


19 


ment (for example in three space dimensions). 
A number of generalized applications will be 
found in this report. 


1 FEEDBACK IN GENERAL 

Operations which form, in the causal sense, a 
closed sequence or chain, and which thus occur 
in a completed ring or loop, form a special 
branch of dynamics of great importance in 
many aiming controls, as well as in controlling 
and regulatory devices generally. Such causal 
loops may be entirely automatic in nature, or 
may contain one or more human elements as 
an essential connecting link. A variety of 
terms, such as feedback, retroaction, regenera- 
tion, and degeneration, have come to be applied 
in the identification of systems which are so 
constructed; a servomechanism is basically of 
this character. 

The most important property of such a 
physical arrangement is the stability with 
which it operates. In cases where the com- 
ponents and the interconnections involved are 
linear, that is to say where the principles of 
additivity or superposition for cause and effect 
apply, the criteria and the instrumental strat- 
agems for stability are now quite well under- 
stood, and a good body of literature has accu- 
mulated on this subject. The power of feed- 
back processes, thus restricted, is considerable. 
They are applied for a variety of computa- 
tional purposes, as where a characteristic is 
to be reciprocated or inverted, and, for exam- 
ple, in certain complicated problems of smooth- 
ing and prediction. 

On the other hand when nonlinear compo- 
nents are involved, and where consequently 
the additivity principle is violated, as in gen- 
eral with a human operator forming a con- 
necting link in the loop, a considerably more 
recondite situation is attained. Beyond the in- 
ferences which are available from linear ap- 
proximations, and which must be very care- 
fully drawn, the major recourse for such ques- 
tions must be to experimental methods and to 
model studies. We refer for example to the 
methods of simulation treated elsewhere. 

For purposes of broad reference, and to set 
down concretely a rather purified example of 


the feedback phenomenon, we give here briefly 
what may be considered the simplest and hence 
the most fundamental system in which feed- 
back is involved. There is intended to be noth- 
ing new in this. 

In the accompanying figure, the operator 
being the characteristic in the “box,” is of ar- 



Figure 8. Elementary feedback loop or following 
system. 


bitrary nature and is merely assumed to con- 
nect dynamically the incoming and outgoing 
variables. Thus the operator ^ is a physically 
realizable functional which determines the lo- 
cal output as a function of the time t when the 
local input is predicated as a function of time. 
The input variable q = q(t) is arbitrary. The 
output of the box is the variable r, which is 
also the “response” to the operation $ when 
performed on the input to the box. Further, the 
variable u is the “unbalance” or difference be- 
tween q and r. Thus 


u = q — r, 

(37) 

r = ^ • u. 

(38) 

Consequently 

1 

II 

(39) 

and 

1 

II 

(40) 


When the operator # is linear, expressible, for 
example, as a rational function of the deriva- 
tive operator p then under appropriate re- 
strictions we may write 


u = 


and 


I + 4> (p) 


(41) 


4>(p) 


(42) 


In equations (41) and (42) appear the fa- 
miliar operators of linear feedback and servo 
theory. The roots of the rationalized denomina- 


( ^xfidextI a^ 


20 


GENERAL THEORY OF AIMING PROCESSES 


tors of these operators are significant to sta- 
bility, while the merits of ‘‘performance” are 
obtainable in terms of the results of the entire 
operation when q{t) is specified. Stability may 
also be studied, still under the linear restric- 
tion, through the exploration of $(p) itself, 
either experimentally, or analytically in the 
complex plane by the methods of Nyquist, 
Black, et al. If linearity is not clearly indicated, 
the expressions (39) and (40) are to be pre- 
ferred. 

A meaningful interpretation of the closed 
causal system of Figure 8 may be given as 
follows. Suppose it is required to duplicate q, 
which represents, for example, a variable 
weight in the pan of a balance. If then the 
response r is proposed as such a “duplicating” 
variable, the unbalance u indicates continually 
its failure in this regard. The operator 
which may now be considered a “follower,” 
adjusts r through interpretation of the un- 
balance u. Thus the response r is a measure, 
better or worse, of the arbitrarily variable 
weight q. In more general cases the follower 
may have to operate through an additional chain 
of components, and q may contain irrelevant 
signals, and so on. An example of such a “feed- 
back” following operation was given in Sec- 
tion 1.8. We remark that all cases of feedback, 
by proper identification of the input quantity q 
and of the following operator reduce to this 
simple example. 

1 INSTRUMENTAL CONSIDERATIONS 

We wish to include, while on the theoretical 
plane of the present chapter, some remarks on 
the general instrumental character of a fire- 
control system such as has been developed in 
some quantity for airborne application. 

It should be pointed out immediately that 
such a system is typically only part of a more 
inclusive system which may encompass also 
the vehicle in which the apparatus is borne 
and the man or men who manipulate both. 

A fire-control system, or a connected group 
of instruments forming means for the control 
of aim in an airplane, may be divided into three 
parts. One subdivision will be constituted of 
apparatus which feeds in all primary data. 


Such data include continuously measured vari- 
ables, which may be supplied either directly or 
through power-boosting servos. Feedback sys- 
tems may be involved in the measurement of 
the input variables, where, for example, null 
methods are essential to attain a dynamically 
faithful replica of the physical quantity which 
is sought. Other input data may be supplied in- 
termittently or periodically, and these data may 
arise either automatically or by the manual 
settings of a principal operative or by those of 
one of his confederates. The precision with 
which the primary inputs must be supplied, 
for a given aiming accuracy, is a prime prop- 
erty of the system as a whole, or rather of the 
principle on which it functions. 

Another subdivision of the typical fire con- 
trol is that which performs the computation 
which is required, and in which the various 
input data are correlated, collated, operated 
upon, and interpreted with regard to their 
significance to the problem at hand. The com- 
ponents of this subdivision must constitute a 
mechanization, or physical embodiment, of the 
equation or equations which describe the 
method employed for the control of aiming. The 
computation involved here may be algebraic, 
geometric, or may require equipment versed in 
the calculus. In general the mathematical op- 
erations performed are nonlinear, although in 
a good many cases linear approximations suf- 
fice and are employed. Errors in computation 
arise from a number of sources, and their allow- 
able limits is one of the important specifications 
for this subdivision of the system. Such varia- 
bles as temperature and acceleration may be 
inadvertently “measured” by the computer, and 
it is important to predict such effects and thor- 
oughly to test their final magnitudes. The out- 
puts of the computing subdivision are princi- 
pally the presentation variables, which are 
handed on to the next subdivision. We note that 
some of these variables may return to the ini- 
tial subdivision and may in turn become input 
data for the computing subdivision itself: this 
occurs where it is to make use of a feedback 
stratagem in the realization of certain dynamic 
characteristics, or again simply where servo 
methods are required for the effective delivery 
of a significant variable for the presentation 


INSTRUMENTAL CONSIDERATIONS 


21 


subdivision. Further outputs, or results of the 
computation, may be locally displayed at the 
computer for auxiliary purposes such as check- 
ing and calibrating, or for warning indicators 
of various sorts. These, however, in a liberal 
sense, may also be thought of as presentations. 

The final subdivision, for presenting the ap- 
propriate variables to the one or more opera- 
tors, accepts such variables from the computer 


FEEDBACK PATHS 



Figure 9. Major subdivisions of fire-control system. 


and converts them into a manifestation which 
is perceptible to those individuals or mech- 
anisms. This equipment may consist in a simple 
reflecting sight, an oscilloscope screen, or may 
involve complex follow-up or feedback compo- 
nents whereby null methods are applied to put 
into effect the final consummation intended. 
In many cases an alignment is to be carried 
out between a moving index and a target (or 
alternatively this operation be involved in the 
primary data subdivision). All variety of com- 
binations are possible and have been in evi- 
dence. In manipulating the vehicle to obtain 
a match between his optical presentation and 
the target, the pilot of a fighter supplied with 
an aiming-control system will produce angular 
rates which are introduced into the computer 
and affect the presentation, and hence the 
pilot’s manipulations, and so on around the 
major causal loop which is then involved. The 
stability of tracking which results, and which 
in turn may affect the accuracy of fire, is of 
primary concern ; and a central problem in the 
art is that of so constructing the dynamics of 
the aiming-control system that this process 
will be rapid, stable, and precise. 

To return to the initial subdivision, which is 
responsible for supplying the data to the com- 
puter, we should point out that certain remote 
controls are there to be included which might 
not normally be considered as related to the 
input variables as such. Examples are: adjust- 
ments of the computer which depend on the 
type of airplane involved; settings made by 


the pilot in indication of his choice of projec- 
tile; and the firing operation itself, which may 
require resetting of the computing components 
for the next attack. 

Note further that although the excellence of 
a control or of a computing system depends 
pivotally (aside from considerations of size, 
weight, permanence, and so on) on the partial 
derivatives of the firing errors committed, 
taken with respect to the errors in the input 
data, it depends as well on the inherent accu- 
racy with which such input data may be sup- 
plied. Thus if range, for example, may be 
measured with great precision, relatively 
speaking, it is less important that a given 
system or principle of operation be insensitive 
to this particular input variable. In such con- 
siderations, statistical methods are supremely 
useful, although great attention is warranted 
to the assumptions made in any given case; to 
pass beyond the region of validity of these as- 
sumptions deserves and should receive severe 
criticism. 

A few remarks are here warranted on some 
of the commoner variables which are continu- 
ously measured in an airplane for the purpose 
of aiming controls. Briefly these comprise: 
distances, velocities, , and accelerations ; and 
angles, angular rates, and angular acceleration. 
The passage of time itself should be added. 
Such quantities may be measured directly, or 
obtained by inference from related quantities. 
For example a velocity may be measured as 
the integral of the corresponding acceleration. 
We mention as follows, however, only the 
primary measurables themselves. Distances 
are frequently obtainable, to appropriate ob- 
jects, by radar-ranging methods. Altitude as 
ground clearance is included, although the 
barometric pressure may contribute with other 
measurements to a knowledge of the altitude 
over an appropriately defined point. The so- 
called indicated airspeed may be measured in 
terms of the difference between dynamic and 
static pressure, and may be converted to true 
airspeed through auxiliary measurement and 
computation. Accelerometers, in a variety of 
forms and excellences, will provide measure- 
ments of the acceleration of the airplane in a 
coordinate system fixed therein or, by appro- 


tCONFIDENTIA 




22 


GENERAL THEORY OF AIMING PROCESSES 


priate stabilization (which may be considered 
to involve measurements of angle), with re- 
spect to an unaccelerated coordinate system. 
Angle is usually measured with respect to fixed 
directions, these being manifested by free — 
or approximately free — gyros. Absolute di- 
rections are provided by North and Down, 
and these represent long-term standards. An- 
gular rates, of the vehicle or of independent 
platforms therein, may be given extremely 
quickly and accurately by captured gyros, 
which are discussed elsewhere (particularly 
in Chapter 3). Finally, angular accelerations 
are provided through the measurement of 
torques on a body possessing rotational inertia. 

We have referred above, and purposely so. 


to a relatively complete fire-control system. 
The opposite extreme is represented by the 
warrior who fires ''by eye,” and who by dint 
of training and experience has developed aim- 
ing controls in his judgment and in his re- 
flexes. This procedure, which can lead to re- 
markable precision, has attained however an 
unfortunate aspect of glamour, and has very 
definite limitations for modern operations. Most 
aiming controls extant, and these are far from 
perfect, lie somewhere between these two ex- 
tremes. Thus, there are numerous cases where 
automatic apparatus combines with visual esti- 
mates, as of the speed of a warship, the duration 
of a brief time interval, or the angular depression 
of a target below the horizon. 


K )NFII)ENTIAL 


Chapter 2 


ON CERTAIN ASPECTS OF TRACKING 


2 1 TRACKING AND OUR CONCERN 
THEREWITH 

B y ‘‘tracking’' is here meant a continuous 
following or alignment procedure which is 
pursued through cognizance of its error or 
unbalance, as in the basic feedback or follow- 
ing operation described in Section 1.10. A good 
example, although somewhat abstractly dis- 
closed, is given in Section 1.8, where an arbi- 
trarily varying position vector is to be followed 
by an artificially generated position vector 
which is infiuenced by manipulation of an in- 
tegration constant and a velocity. 

Tracking pervades all branches of fire con- 
trol, but it arises principally in aiming opera- 
tions as such, whether these be manual or au- 
tomatic. With regard to the latter, automatic 
tracking is essentially indistinguishable from 
other types of automatic control and will here 
be considered in that light. However, our major 
interest in the present chapter is in tracking 
by manual means, a human operator being in- 
volved. While the removal of human limita- 
tions gives the greater promise to automatic 
tracking devices and techniques, still there is 
a good bit to be learned, even for such un- 
limited future trends, from tracking of the 
human variety. Besides this, the human ele- 
ment can hardly be altogether eliminated, 
even ultimately, and until we give to our ma- 
chines the final powers of judgment and choice 
we shall find it necessary personally to direct 
their efforts. It may also be doubted that the 
adaptability or educability of the brain, where- 
by it adjusts to altered circumstances, can soon 
be imparted to the automaton in any but the 
most trivial of cases. Or rather, if this is to be 
done, it will probably be through imitation of 
the processes by which such adaptations take 
place in the animal mechanism. 

It is typical of the writer that he con- 
siders the entire subject of tracking to come 
within the broader boundaries of regulatory 


controls, which to him include all corrective 
apparatus having a closed causal loop. In this 
connection, and although the region has not 
been very far explored, there will be traced 
out briefly in what follows an analogy between 
the past development of automatic regulators 
and that of tracking aids. From this analogy 
a deduction will be made as to the future of 
the latter field of endeavor. Aside from this 
conjectural activity, we have been intimately 
concerned with tracking in a number of de- 
velopment programs where fire-control ap- 
paratus was being devised. Tracking in range, 
and we speak now of manual tracking, 
whether by stadiametric means or otherwise, 
has not entered particularly into our imme- 
diate sphere, and it is further evident that this 
brand of tracking has been dealt with very 
thoroughly by other groups. Thus it may be 
said that tracking in angle, or more precisely 
in direction, is under discussion. The problems 
and technology of such tracking have appeared 
in gunnery systems, and in those for bombing, 
guided bombing, and for airborne rockets. 

For flexible gunnery, an elaborate instru- 
mental, statistical, and psychological study of 
the man-machine interactions which tracking 
comprises was undertaken and pursued by 
Section 7.2 at The Franklin Institute. This 
project (NO-268) dealt with standard types of 
computing dynamics and with known kinds of 
aiding controls. Many significant results were 
obtained; some unexpected. Other members of 
the section have been more directly involved, 
however, and their writings should be referred 
to rather than the present material. (See Part 
III, for example.) While allusions may be 
made here to this work, it will not be further 
discussed or described. 

2 2 the human FOLLOWER 

People “track” during every conscious mo- 
ment, unless their eyes be closed, their hands 


^CONFIDENTIAL f 


23 


24 


ON CERTAIN ASPECTS OF TRACKING 


tightly tied, and their tongues clamped solidly 
between their teeth. Alignment processes, in 
which the alignment error serves as datum for 
its own annihilation, are forever being car- 
ried out in the familiar operations of living. We 
may thus expect that there is a rudimentary 
sort of tracking circumstance in which the 
human operator will be at home, and in which 
he will be found to be greatly and innately 
skilled. Pointing at a moving object with a 
pencil, or with a rifle under beneflcial condi- 
tions of support and inertia, is a tracking 
operation which may be carried out relatively 
well. Provision of a reflecting sight, or of a 
nonmagnifying telescope with cross hairs, does 
not improve the operation extensively and has 
even been seen to impair it. Of course it is a 
different matter with magnification, since then 
visibility and visual resolution may be vastly 
increased. This is not to say that this '‘nat- 
ural” type of tracking cannot be improved 
upon, for in tracking targets which are chang- 
ing very slowly and uniformly an adjustable- 
rate device is superior, this being only one 
example, but on the whole for typical cases, 
and where scale factors in the presentation are 
reasonably adjusted, such natural tracking 
would suffice admirably. It is assumed here 
that closeness of tracking as such is desired, 
or simply smallness of tracking error. It is 
evident that for the larger purposes of aim- 
ing contol this is not the only index of ex- 
cellence. The needs and nature of the inter- 
pretative and computing equipment cannot 
finally be separated from those of the track- 
ing controls. We are thus discussing a sub- 
sidiary problem, but more on this again. 

We repeat, those tracking arrangements 
would suffice in which the dynamic relation- 
ship between the immediate manual manipula- 
tion and the direction index were of the same 
character as in the arrangements referred to 
as natural. If this is an overstatement of the 
case, then we should like to assume that there 
might be discovered some even more ideal dy- 
namic connection between the manual manipu- 
lation and, say, the visual index, and that the 
dynamic nature hereof might be expressible in 
quantitative form, even though the ideal dif- 
fered from one individual to the next.^-^ 


2 3 the causal loop 

It is frequently pointed out that the elements 
in a tracking system form a chain, and that 
consequently each element must perform as 
perfectly as the whole assemblage is intended 
to perform. But it has not been sufficiently re- 
iterated that these elements form a closed 
chain, or a complete loop, together with the 
human operator, where one is present. This 
fact brings to the tracking process all the spe- 
cial characteristics, including the unique con- 
ditions for stability and periodicity, which are 
peculiar to that type of system. The formation 
of such a loop, in the causal sense, is particu- 
larly significant when there is included the 
dynamic characteristic of a “disturbed” or 
lead-computing sight, so-called. For in spite 
of the fact that the little understood dynamics 
of the human operator are included, many of 
the properties of those loops which are en- 
tirely automatic, and which are familiar in 
automatic regulatory devices and in many au- 
tomatic controls, are seen to be present in the 
tracking sequence. It seems evident that an 
approach to the tracking problem, thinking of 
this problem as requiring the provision of im- 
proved aiding equipment, would best be made 
a basis of the recognition that the operations 
involved are of this cyclic character. Opera- 
tions in a closed loop are fundamentally dif- 
ferent from those in an “open” or “straight- 
through” system. Both advantages and dis- 
advantages follow from such an arrangement, 
and this will define our principal topic. We wish 
first to map out the causal circuit involved in 
a tracking system in operation. 

Suppose a directional index is to be made to 
coincide, as nearly as possible, with the direc- 
tion of a target which has motion only partly 
predictable. We shall assume at first that such 
motion may also be contributed to by motion 
of a vehicle from which the tracking is taking 
place; that is, tracking is to be in vehicle co- 
ordinates. At any rate there is a dynamic con- 
nection to the directional index (or sight index) 
from some sort of handle or control which is 
under direct manipulation. If a coordinate }x 
is assigned to the displacement of the handle, 
and a (for reasons later to become evident) to 
that of the sight index, then the tracking dy- 


THE CAUSAL LOOP 


25 


namics are expressible as a relationship be- 
tween these two variables coordinates, or as 

a = T • n, (1) 

where T is what may be called the tracking 
operator. Note that in general T may be a 
nonlinear operator, whereas in the analytically 
manageable cases it is linear; at worst, linear 
approximations serve admirably as rational- 
ized ideals. When thus rationalized, T = Tip). 

We should state that the coordinates such 
as fx and a, which are used here, may be con- 
sidered as multiple-valued quantities, as vec- 
tors that is, or again simply as one of the com- 
ponents of the problem, in circumstances in 
which such a one is representative and in 
which a significant and symmetrical such sepa- 
ration into components is possible. 

Now the sight index ^ is to be compared 
with the true sight direction or direction to the 
target, which may be given the symbol a. 
Thus the difference between these two, or the 
error, which is visible to the human operator, 
is an important variable. We define the error 
e as 

e = a — a. ( 2 ) 

While under ideal tracking this difference will 
remain identically zero, still in real operation 
its value must be continually observed and in- 
terpreted to approximate this ideal. 

Perception, we assume by visual means, of 
the tracking error c, and manipulation of the 
handle /x on the basis of such perception, is the 
office of the human operator. Symbolically, 

n = H • e 

where the operational symbol H presumes to 
embody what takes place functionally be- 
tween the eye and the hand. This operator 
must thus include not only the delicate reflexes 
and inhibitions of the human nervous system, 
sensory, motor, and as much of the central 
system as may be involved, but also the ran- 
dom excitations and “nervousness” which are 
characteristic of the organism. It must embody 
further, for complete representation, the abil- 
ity to learn,'^’* which implies a fundamental 
nonlinearity. 

The causal loop should now be quite distinct, 
from eye to hand to sight index and around 


again, continually and cyclically. Figure 1 
shows this circuit in symbolic form. It will 
readily be seen, by comparison with Figure 8, 
that the operators H and T, in series, corre- 
spond directly to the follower-operator 4> of 
the latter figure. Before passing on to a more 
detailed consideration of the components which 
may, in relevant cases, be involved in the 
causal loop of tracking, a few words should 
be spent toward clarifying what is to be gained 
by recognizing the existence of the loop as an 
essential feature of the whole phenomenon 
under discussion. In dealing perpetually with 
equipment which operates in this sort of closed 





causal connection, as one does with servomech- 
anisms and with regulatory mechanisms gen- 
erally, a number of special characteristics come 
to be familiar which are peculiar thereto, and 
which are not typical of all arrangements. One 
such characteristic, having to do with the de- 
cay of transients, is that such decay occurs 
quite uniformly among all the variables which 
are directly included in the loop. This is evi- 
dent either by analytic considerations or from 
observation of the operation which is typical 
of such systems in practice. That is, if the 
parameters of the various components of the 
loop are so adjustable in their mutual rela- 
tionship that any one of the variables of the 
system subsides stably and rapidly to an equi- 
librium condition following the imposition of 
given initial conditions, or following a tran- 
sient disturbance of any type, then all of the 
variables directly included around the loop 
will subside stably and rapidly for the same 
adjustments. This is not true for open chains 
of components, for example, and is but one 



aiKFIDENTIAL 


26 


ON CERTAIN ASPECTS OF TRACKING 


of the properties unique to causally closed ar- 
rangements. One consequence of this property 
which may be worth citing is as follows. While 
the precision itself of tracking, in a director 
system where the sight index is not derived 
from the final aiming operation, may not as- 
sure accuracy in the latter operation owing to 
the response of an intermediate computer to 
other characteristics of the tracking, a very 
different circumstance holds true for the dis- 
turbed-sight type of equipment. Here the closed 
system, as explained above, keeps the dynamic 
performance of gun and sight index, as varia- 
bles of the loop, much closer together, and an 
adjustment which makes for better tracking 
more nearly succeeds also in giving a corre- 
sponding improvement in aiming than is the 
case with a director. The present argument is 
admittedly qualitative, but the facts are borne 
out by the quantitative data which have been 
obtained. We are indicating only a mode of 
thinking; it remains to be put to more articu- 
late use. It is recognized further that these 
arguments may by now have become trite in 
fields of which the writer has little knowledge. 
His own interpretations of need are based, 
naturally, on the work he has seen in progress. 

2 4 FURTHER BREAKDOWN OF THE LOOP 

Speaking particularly of the lead-computing 
or disturbed sight, so-called, we wish to illus- 
trate, through elaboration of the operational 
tracking circuit of Figure 1, the principal dif- 
ference between the uses of such computing 
components and of those which occur in direc- 
tor systems. Thus in Figure 2 the two general 
classes of systems are given, in the one case 
the tracking function T of Figure 1 breaking 
into the series components A and S, and in the 
other the sight index ^ being accepted by an 
independent channel. In each case the symbol 
y stands for the coordinate of the gun, say, or 
for that of whatever direct aiming agent gov- 
erns the initial direction of the projectile. The 
component C, in the lower portion of Figure 2, 
besides computing the “kinematic lead’' for the 
gun on the basis of the dynamic behavior of 
a and of the range to the target, applies what- 
ever additional ballistic corrections are essen- 


tial, including parallax, for example. Owing 
to the rich literature which is available for 
director systems, beyond anything we can in- 
clude here, and to the rather different nature 
of the smoothing problem (in which transients 


COMPUTER 



DIRECTOR 


COMPUTER 




Figure 2. Positions of computer with respect to 
tracking loop. 

in a are to be kept from harmfully affecting 
y), we shall deal henceforth with the system 
in the upper portion of Figure 2. Further ref- 
erences, however, may be made to director 
systems in the present report, but these will 
be conjectural only and will show possibilities 
for future development rather than being de- 
scriptive of work we have followed. 

Speaking basically, it is as legitimate to 
achieve a given dynamic relation between the 
gun coordinate and that of the line of sight to 
the target by means of the upper system of 
Figure 2 as by the lower one, the most mani- 
fest difference being the inclusion of the dy- 
namic gun-to-sight computing function, in the 
former case, as a component of the tracking 



AUTOMATIC REGULATORS AN ANALOGY 


27 


loop. Whereas, in that case, the power require- 
ments and the inertias of the gun itself may re- 
strict the mobility of the tracking loop, it is 
evidently possible to replace the variable y 
in this loop by a lightweight and lower-power 
mock gun or index y, and then separately to 
reproduce y, in the real gun coordinate y, as 
effectively as the external high-power controls 
will permit. As in the director, such corrections 
as trail and parallax may be additively included 
in this final transmission, which is not then 
part of the loop. 

We now consider only the upper system in 
Figure 2, where the variable y may be manipu- 
lated without the restrictions which a heavy 
turret (or an airplane) would impose. What is 
the best characteristic for the “aiding’’ opera- 
tion A? First assume that there is a satisfac- 
tory form for the tracking function T, and 
that this form T' is linear, so that T' = T"(p). 
This is either the “natural” form spoken of 
above or some “idealized” version thereof. Un- 
der the relevant exterior circumstances, sup- 
pose that this form T'(p) of the tracking func- 
tion or operation will produce a very close 
alignment of ^ with o-. It is then evident that 
if the computing function S is such as to give 
rapid and accurate performance when <7 ~ o- 
(nearly), that it is only necessary to make 
A ip) Sip) = T'ip), where it is assumed that 
A and iS are linear, although their parameters 
may vary with the time. Thus an ideal, or 
nearly ideal, form for the aiding function is 
given as T'ip)S-^ip). Since T is certainly not 
critical, one would suspect that this new value 
for A need not be critical. Reasonable approxi- 
mations should suffice. 

2 5 AUTOMATIC REGULATORS - 
AN ANALOGY 

There is a remarkable parallelism, histori- 
cally, between the development of tracking aids 
and the progressive steps which have been 
made in the types of automatic regulatory 
equipment for commercial processes. This is 
not altogether surprising, since both involve 
the gradual perfection of components which 
are added to apparatus operating in a (caus- 
ally) closed loop, and since both have as purpose 


to improve the stability and performance, in a 
special task, of the systems to which these 
components are added. In discussing tracking 
aids we are referring for example to the com- 
ponent A in Figure 2. 

It is not a far cry from the tracking loops 
shown above to the regulatory loop of Figure 


MANIPULATED 

VARIABLE^ 

REGULATOR "PLANT" 

m 



DESIRED BEHAVIOR 
OF V 


UNREGULATED 
BEHAVIOR OF V 


Figure 3. Symbolic reiiresentations for regulatory 
control loop. 


3, where the components are given in sym- 
bolism recently recommended to the ASME by 
a Committee on Symbolism for Industrial 
Regulators and Controls. Here the regulator g 
may be considered to correspond approximately 
to the A component of Figure 2, whereas the 
plant h may correspond to the components H 
and S, in series, of the latter figure. Both H 
and S, in typical cases, involve lags or char- 
acteristics responses which fall off in amplitude 
at the higher frequencies. The typical plant 
also involves lag, which generally makes for 
difficulty in regulation, and requires advanced 
forms for the dynamics of the regulator. But 
we proceed with our analogy. 

The dynamic characteristics of velocity 
tracking, displacement tracking, and aided 
tracking, as these names have come to be used, 
may be illustrated by the responses, for exam- 
ple, in the gun coordinate y when a step input 
is applied to the handle /a. Thus, in Figure 4, 
the responses shown by curves a, h, and c as 
functions of time are characteristic of the 
classical tracking dynamics in the order named 
above. Now these same responses happen also 
to characterize the dynamics, such as would 
occur between the measured unbalance and the 
manipulated variable of Figure 3, of the classi- 
cal regulator types as they occurred in his- 


CONFIDEN1TAU 




28 


ON CERTAIN ASPECTS OF TRACKING 



torical order. These are called, respectively, the 
floating (or integrating) regulator (or con- 
troller), the proportional regulator, and the 
proportional-plus-floating regulator. The lat- 
ter, like aided tracking, proved to constitute a 
big advance when it became generally avail- 
able. It is now interesting to conjecture whether 
a more universally potent regulator character- 
istic, such as the newer one which leads to the 
response d of Figure 4, would correspond to 
an improved tracking function. To the writer 
it seems that the evidence of the analogy points 
unmistakably in that direction. 

A word more : In the cases both of tracking 
and of the regulator problem, one deals not 
with systems in which the remainder of the 
loop is of well-known and identifiable dynami- 
cal character, but with systems in which that 
portion of the loop is rather vague and change- 
able. Thus the human operator is hard to de- 
scribe, not only by virtue of the intricate na- 
ture of its response at any given time, but 


also because this nature changes in time in 
dependence on conditioning and on fortuitous 
causes. So in the regulatory case, the regulator 
must cope with an ill-defined mechanism, and 
must be flexible for initial adjustment and non- 
critical for continued effectiveness. It is tempt- 
ing to suspect that both fields are now only in 
rudimentary stages of development. 

2^ CHARACTERISTICS OF 

HIGHER ORDER 

We have a circumstance in tracking in which 
it is likely that more elaborate dynamics will 
lead to greater effectiveness when the human 
operator and the kinematic computing equip- 
ment are included together in the tracking 
loop. In Figure 4, the response d implies a dif- 
ferential equation of higher order than do the 
preceding responses (a, &, and c). In the tech- 
niques of automatic regulation, it is a familiar 
experience to find that the extra degree of free- 
dom which is permitted by passing to a higher- 
order regulatory law enables an adjustment of 
the parameters which offers results, in stability 
and performance, far beyond those obtained 
with the simpler arrangement. Along with 
such an increase in complexity, for its man- 
agement to be possible, must come a knowledge 
of how to handle the new complex of adjust- 
ments, and how consequently to exploit the 
generalized dynamic adaptability which is at 
hand. In the field of regulation such knowledge 
was acquired, but the analogy with tracking 
aids is as yet somewhat less distinct than that 
traced out in the last section. 

With regard to the familiar classical dy- 
namics of the lead-computing sight, there are 
several reasons to suspect that a characteris- 
tic of higher order would serve more effectively. 
This is true on the one hand through the 
straightforward argument that linear predic- 
tion, here in angle, should properly be general- 
ized to a prediction of higher order, since the 
typical engagement involves acceleration of 
relative target motion. We enter here into a 
basic controversy which is familiar in ground 
and seaborne equipment. Further, however, in 
the coupling constant of the lead-computing 


ONFIDENTIAI^ 


MULTIPLE SIGHT INDICES 


29 


sight, which, in addition to the thus far un- 
avoidable adjustment for time of flight, is the 
only adjustable parameter of the computation, 
an extremely crude compromise has been nec- 
essary, especially in the presence of the availa- 
ble tracking dynamics. Adjustment of the 
coupling constant in one sense gives an im- 
proved stability of tracking, and in the other 
sense gives a more rapidly decaying transient 
error in the computation. The region of over- 
lap does not lead to great satisfaction on either 
score, and a very shallow optimum, in terms of 
gun error, is shown on exploration of this sin- 
gle adjustment. This is precisely the sort of 
situation which is typical of regulatory cir- 
cuits, and for which very frequently a more 
articulate dynamic characteristic has stepped 
in to put the whole affair on a new basis. For 
example, in many regulatory cases where a 
regulator of first- or second-order dynamics 
has been used, and in the adjustment of which 
unsatisfactory compromises must be accepted, 
the insertion of a higher derivative term in the 
regulatory dynamics can sever the interde- 
pendence of parameters which necessitates 
the compromise and can allow a readjustment 
giving the results which are in an entirely 
new class. 

Now it may be noted that the characteristics 
of the aiding component and those of the kine- 
matic computer are intimately related in the 
tracking loop. There is thus, in view of the 
possibilities for improvement indicated above 
for each component, an even more striking 
possibility that a mutually beneficial restyling 
might be carried out jointly between the two 
together. A proposal involving this sort of in- 
novation was made^ for application to the case 
of a lead-computing sight as used in a velocity 
tracking turret. This proposal was only for a 
minor change, and was premised on the possi- 
bility that a physical alteration of simple form 
might improve circumstances, but it did result 
in a conversion both of tracking function and 
of the lead-computing dynamics, and to higher 
order. While never actually applied to full- 
scale trial installations, it was reduced to simu- 
lative form, and enough work was done to 
indicate a possible improvement. It is evident 

"By H. Whitney. 


that this is not an unpromising history in view 
of the embryonic status of such modifications.^ 

2 7 MULTIPLE SIGHT INDICES 

There have been several examples, which to 
the writer’s knowledge have first appeared over 
the past three years, of the employment, in 
aiming controls, of sights or directional sight- 
ing means in which multiple indices occur. It is 
considered that an important new technique is 
embodied in these, and that it is worth while 
briefly to sketch out what they involved. For 
simplicity we restrict the discussion to visual 
aiming equipment; the developments referred 
to, as it happens, have been similarly restricted, 
although the underlying principle is certainly 
more general. 

The examples referred to above shall now be 
mentioned. First, in the British method for 
low-altitude angular rate bombing, as embodied 
in their LLBS Mark III, a row of collimated 
luminous lines, parallel and equally spaced, was 
rotated downward with respect to space. The 
lines were oriented horizontally, and the opera- 
tor merely observed the target through the 
optical grid thus formed. When the target, 
which at first appeared to be progressing ‘‘up- 
ward” across the lines, became momentarily 
stationary with respect to the grid, the opera- 
tor acted on this instantaneous synchronism 
as his signal to release a bomb. 

Second, in the proposal for the so-called 
Texas sight, of which models were built and 
tested on the ground, a constellation of lu- 
minous points was substituted for the single 
collimated reticle of the classical lead-comput- 
ing sight. The points of the constellation, 
which formed an extended two-dimensional 
pattern in angle, moved with the single reticle 
and converged exponentially toward it as fo- 
cus. Ideally, it should be added, the points of 
the pattern should not rotate about the central 
one; not with respect to space, that is. In use, 
the operator merely manipulates his tracking 

‘’We refer, however, to the writings of H. Whitney on 
tracking, and to the more detailed accounts of simula- 
tive tracking studies which were carried out under Sec- 
tion 7.2 at Columbia University and at The Franklin 
Institute. 


‘'By L. LaCoste. 


QoONFTfaENTBlr^ 


30 


ON CERTAIN ASPECTS OF TRACKING 


controls, or the gun itself, so as to achieve 
equality of angular velocity bet^veen the tar- 
get and the local points of the pattern. Two 
results ensue; for one thing it is far easier to 
track, since an integration is omitted from the 
tracking loop, the operator observing rate 
rather than position; furthermore the oppor- 
tunities to fire are multiplied tremendously, 
since as may easily be demonstrated the suf- 
ficient conditions as well as the necessary ones 
are given for effective fire. The trouble has 
been that a visual stadia for manual ranging 
was difficult to incorporate along with the op- 
tical pattern, but this circumstance might be 
altered in view of modern ranging facilities or 
of the use of methods in which range is not ex- 
plicitly accounted for. 

A third instance of the need or desirability 
for many sighting indices has been involved in 
the writer’s proposals (Section 10.3) for tech- 
niques to be used in the pilot’s universal sight- 
ing systems [PUSS] (Project NO-265) and in 
certain optical systems for the control of 
guided bombs from a static position at ground 
level (Chapter 8). In both cases the tracking 
display would be similar to that in the two in- 
stances already mentioned. In neither case has 
the method been finally reduced to practice. It 
will suffice to mention here a simple means for 
arriving at a collision course. 

It is well known that if the axis of a free 
gyro in a vehicle, for example, be initially 
pointed at a target, and that if subsequently 
the vehicle be so steered that the axis continues 
to point at the target, then a collision course 
will result subject to the conditions described 
already in Chapter 1. Now this criterion for 
steering is not an easy one, and to achieve 
stability it is evident that coupling must be in- 
troduced between the heading of the vehicle 
and the line of sight. Instead of this, an im- 
proved stability would also result if uncoupled 
lines of sight were displayed as a pattern in 
every direction, through one of the several 
available means for such stabilization and 
presentation. Transient errors would not need 
to be corrected all the way back to the start- 
ing point, it being essential only to keep those 
points of the pattern moving with the target 
which are already in proximity therewith. The 


stars themselves, if sufficiently dense, would 
serve admirably as such a pattern. It is not 
known by the writer if they have ever been 
so used. 

2 8 TRACKING BY THE PILOT 

In fixed gunnery, aerial torpedoing, bombing, 
and rocketry a pilot may be expected to carry 
out an aiming process which involves keeping 
an artificial line of sight, either fixed or 
moving with respect to the airplane, in ap- 
proximate coincidence with the line of sight 
to the target. The pilot employs the normal 
flying controls in this operation, and in so do- 
ing deals with a system of tracking dynamics 
which differs radically from, and at the same 
time is considerably more complex than, the 
controls which are common, say, to a turret. 
For typical airplanes, and for the modes of 
approach which have been in demand, the pilot 
must continue to perform a number of special 
operations which are essential to safe and effi- 
cient flight, and which although they may be- 
come semi-automatic nevertheless provide dis- 
tractions from the efficiency of his tracking, 
as such. Thus he must watch his indicated air- 
speed, keeping this quantity within specified 
bounds, he must trim all his control surfaces 
to maintain any sort of symmetry in his indi- 
vidual manipulations, he must so operate the 
rudder that skid is maintained below an allow- 
able amount, and he must beware the possi- 
bility of flying underwater or underground. 

It is clear that under these circumstances ad- 
ditional tribulations such as manual adjust- 
ments to a computing system or attention to 
complicated warning indicia are unwelcome 
and must be kept to a minimum or eliminated. 
In spite of the stringency of such requirements, 
the single-pilot airplane, principally the fighter 
and the fighter-bomber, has evolved into the 
most useful weapon in the air, and thus has 
deserved attention as a vehicle for which the 
development of aiming controls is a profitable 
pursuit. 

The most striking feature of the tracking 
dynamics available to the pilot is the asym- 
metry in the up-down and sideways directions. 
For pulling up the nose of the airplane, or for 




onfidential: 


MORE ON THE HUMAN TRACKING OPERATOR 


31 


nosing downward directly, a motion of the stick 
forward or backward is all that is required. 
However, and especially if the pilot wishes to 
fly without skid, his operations in manipulat- 
ing the airplane toward a goal which originally 
appeared to one side are very much more in- 
tricate. This is partly true since as he pro- 
gresses in the operation the target does not 
maintain its direction with respect to airplane 
coordinates, but rotates approximately about 
a longitudinal axis therein, first one way as the 
maneuver begins and then the other way as the 
maneuver comes to completion. The pilot must 
operate both stick and rudder, and each in a 
different manner, during such a maneuver. Un- 
der these asymmetrical conditions, it is obvi- 
ously even more complex to point the airplane, 
not to mention a sight index dynamically re- 
lated to the airplane, in a direction which is 
neither directly above or below nor to one side 
of the general direction of flight. For some of 
the problems connected with tracking through 
the controls of an airplane, other chapters of 
Part I may be consulted. Thus in Chapter 4 
a laboratory apparatus is discussed in which 
the phenomena of such tracking are repro- 
duced electronically in the laboratory. Again in 
instruments for aiming rockets and for multi- 
weapon aiming instruments, the special re- 
quirements which arise from the nature of 
tracking by the pilot are dealt with. 

Although no apparatus has yet been pre- 
pared for this purpose, it is of interest to dis- 
cuss a possible means for use by the pilot in 
tracking which has been seriously proposed** 
and which may be prophetic for future systems. 
There are analogous arrangements which have 
been proposed and tried out for bombers and 
for automatic missiles. 

The idea is for the pilot to track the target 
through an independently stabilized system 
which is carried in the airplane. For such 
tracking he would manipulate conveniently 
mounted controls which would rotate in space 
a sight index having no direct dynamic cou- 
pling to the airplane. This tracking component 
would be expressly designed to assure mini- 
mum error and maximum smoothness in the 
continuous representation of the line of sight 

^For example, in 1943 by Lt. Comdr. E. S. Gwathmey. 


to the target. From the motion of the sight in- 
dex thus developed, with reference to the sta- 
bilized system, all data on angular motion of 
the line of sight are extracted automatically 
and continuously. These data, together with the 
remaining significant variables (speed, range, 
acceleration) are submitted continuously to a 
computing component which determines the 
proper instantaneous heading for the airplane 
in which it can effectively launch a projectile 
at the target. A high-performance automatic 
pilot, given this information, flies the airplane 
in such a manner that the firing condition is 
satisfied. The pilot merely tracks the target 
and chooses when to fire, in which latter choice 
he may be assisted by instrumental means 
which show him the transient condition of the 
computing and piloting operations. In normal 
flight some simple adaptation might be found 
useful for navigating, and would serve to 
lighten the pilot’s responsibilities in any case. 
On retiring from any given engagement it 
might seem appropriate for the pilot to take 
over the controls in the traditional manner; on 
the other hand, he might simply turn his track- 
ing index suddenly away in the desired direc- 
tion for retirement. It would be straightfor- 
ward to incorporate an optionally usable 
automatic evasion. Safety interlocks would 
come into play at minimum ^‘times-to-ground” 
and at maximum ‘‘gees.” 

The remaining steps to complete auto- 
maticity are not unthinkable, even when the 
vehicle becomes a projectile itself. Automatic 
detecting components can lock on the target, 
and computers and automatic pilots can work 
out the attack. With no human pilot, for ex- 
ample, it is no longer necessary to bank. But 
here we enter the field of guided missiles. 

2 ’ MORE ON THE HUMAN TRACKING 
OPERATOR 

It is plausible that for a given state of con- 
ditioning or “learning,” and within certain 
limits, the human operator in the following or 
tracking operation may be considered approxi- 
mately linear. This belief in itself, however, is 
not to be accepted without question ; there are 
a number of queries which are not easy to an- 


CONFIDENTLAL 


f 


32 


ON CERTAIN ASPECTS OF TRACKING 


swer in connection with its justification. Thus 
if the operator is a linear one, why does it not 
react the same each time to a given stimulus? 
How account for random ‘‘dithering”? What 
linear mechanism is there which will exhibit 
these varying states of muscular preparedness 
at the onset of an experiment? Many such 
questions may be parried by pointing out that 
such irregularities may be provided in an au- 
tomatic model by virtue of an artificial source 
of random signals which add directly to the 
output, or elsewhere in the circuit. For example 
they may be thought to arise as the generated 
response to random excitations in the internal 
feedback loops which one includes under the 
name kinesthetic. Or these questions may be 
parried rather differently by indicating that 
the fluctuating components of the human re- 
sponse are unimportant, and need not be rep- 
resented in a linear model since they are rap- 
idly attenuated in the remaining components of 
the tracking loop. This seems to be a particu- 
larly dangerous assumption. In any case the 
closest approximation to a model of the human 
following operator appears to be attained® by 
a linear function, say H(p), together with an 
added random fluctuation, as illustrated sym- 


p (t) 



Figure 5. Model of human tracking operator. 

bolically in Figure 5. We shall consider what 
may be the nature of H{p) which approximates 
most closely to the human example. 

It should be stated first that a considerable 
body of work has been done on this problem 
aside from the very small amount with which 
the writer has been associated. There are ac- 
counts available of experimental and theoreti- 
cal work on this topic, both in Great Britain 
and within Division 9 at Radiation Laboratory 
at MIT. Those titles^’^-^ which the writer can 


obtain are listed in the bibliography for this 
chapter, but it is certain that the interested in- 
vestigator can find these records through other 
channels. In the various linear operators which 
have been proposed there is some uniformity, 
whereas wide disparity seems evident in the 
methods of approach to the problem, and in the 
significance, for example, which the different 
researchers have attached to the method of 
frequency analysis. Our own view on the latter 
question has been that any simple study based 
on the response to simple harmonic inputs, or 
even to the sums of a few such inputs having 
irrationally related frequencies and different 
amplitudes, will admit the possibility of learn- 
ing by the operative under test, with a con- 
sequent fundamental alteration in his charac- 
teristic. The more complex of the composite 
harmonic inputs lead to tremendous difficulties 
in separation and interpretation. 

The primary indication of linearity is that 
generally speaking the observed responses 
double when the stimulus is doubled, provided 
that a limit of apparent “saturation” is 
avoided. Such general proportionality of stimu- 
lus to response is encouraging for the devotees 
of the linear approximation. 

There appear to be only two characteristics 
of the human tracking operator, beyond the 
limited linearity already mentioned and the 
larger fact that over longer periods a learning 
process occurs, which have been at all well es- 
tablished. One of these is the inclusion of lags, 
owing perhaps to the retardations of nerve 
conduction and perhaps again to some more 
mysterious process in the reflex itself. The 
other is the integrating response. Good tracking 
is never deliberated, although it may be de- 
liberate. First, as to lags: It has frequently 
been proposed that these be described by a di- 
rect displacement in time of t seconds, or by 
the effect of the “true” time-lag operator 
exp (— rp). This seems unnecessary on the one 
hand, since nerve conduction is probably not 
distortionless, and it leads to analytic difficul- 
ties on the other hand, owing to the peculiari- 
ties of the time-lag operator. On the basis of 
the known convergence 



®In work done at Columbia' on the possibility of such 
a synthesis, the human operator as such came to be 
known as “Big Henry,” or as H, whereas its model h(p) 
came to be known as “Little Henry.” 




ONFIDENTL 


E 


MORE ON THE HUMAN TRACKING OPERATOR 


33 


it has been proposed^ we could use 

as an approximation to the lag involved in the 
human response. The writer has advocated larger 
values of n as being easily representable in linear 
model, and as probably more nearly representa- 
tive of the situation in nature even than exp 
(— rp) .There is a curious situation here. Psycho- 
logical data give reaction times as a single num- 
ber, but this should not be interpreted as a direct 
time lag. For example the response to a step input 
of the above operator for n = 15 is a transient 
such as shown in Figure 6. If nerve conduction 
were represented by such a lag operator, then 
different absolute thresholds in the indication of 




Figure 6. Response by approximate time lag. 


the response and in the measuring apparatus 
would result in a different apparent reaction 
time for different amplitudes of stimulus, as is 
observed. Notice that the hypothesis of a 
velocity of conduction varying in dependence 
on the strength of stimulus would then be un- 
necessary. To the writer, this explanation 
would be eminently more satisfactory. 

Aside from the lagging response, which is 
certainly a property of the human tracking 
operator, it is evident that there is another 
type of response, which, in addition, may be 

'By Sobczyk at MIT Radiation Laboratory. 


adapted gradually to the environing circum- 
stances. In terms of the coordinate /x of the 
tracking handle as output, and of the observed 
error e as input, and omitting the assumedly 
multiplicative lag-operator, there are reasons 
to believe that an integrating effect, perhaps 
alone and perhaps in combination with other 
effects, is present. 

These conjectures are on the basis of a rela- 
tively simple system around the loop, as when 
the human operator replaces the follower $ of 
Figure 8 of Chapter 1. Admittedly we are dis- 
cussing a human operator which has been con- 
ditioned by the experience of operating in such 
a loop. However, if we knew the character of 
the operator thus conditioned, then, since this 
is a natural circumstance, it would be signifi- 
cant to include compensatory features within 
the loop on the basis of this conditioned char- 
acter if the operation thus modified resembled 
the natural state of affairs. This is not an easy 
viewpoint to express. 

An experiment may be arranged in which 
the operator “follows” a variable by a direct 
manipulation, seeing only the error of his fol- 
lowing. If under these circumstances, during 
the performance and unknown to the operator, 
the error is frozen, the operator simply feels 
that he is exactly compensating for contem- 
porary variations in the input variable but that 
he must correct the accumulated error. The 
very striking manipulation under these condi- 
tions is a continued steady motion in the direc- 
tion which would normally produce such a cor- 
rection. This corresponds substantially to an 
integrating response. 

Numerous experiments, mainly generaliza- 
tions on this simple one, may be carried out to 
determine more precisely what is the operational 
form of the intervening human dynamics. The 
difficulties of frequency methods have already 
been mentioned, but in all cases the problems of 
conditioning warrant extreme care in experi- 
mentation. 

This general problem has been worked on^ and 
the possibility suggested of a purposely estab- 
lished higher-frequency exploratory loop which 
the operator may superimpose on the regulatory 

*^See reference 6 of Chapter 1, also later works by 
Wiener, as yet unpublished. 


TQNFIDENTI^ 


34 


ON CERTAIN ASPECTS OF TRACKING 


loop with which he must deal. This is for the 
purpose of determining the moment-to-moment 
nature of a system which may be changing, or 
for an invariant system (present writer's sug- 
gestion) merely to refresh his memory. Such a 
possibility seems not at variance with the results 
of one British writer who has examined numer- 


ous oscillographs of human tracking. He finds, 
after subtracting out certain lower frequency 
components, that there is a large ‘‘remnant” at 
higher frequencies which has special properties. 
He concludes that the human tracking operator, 
or human servomechanism, appears always to 
operate near instability. 



Chapter 3 


TECHNOLOGY OF ROTATION IN SPACE 


3 1 THE IMPORTANCE OF ANGULAR RATES 

T he measurement and the production of 
angular rates form a fundamental branch of 
instrumental technique in airborne aiming con- 
trols. We distinguish immediately between two 
categories of angular rate: relative and abso- 
lute. In making this distinction it is convenient 
to call up the concept of a fixed direction or a 
fixed body, and to save trouble it is simplest to 
define such a direction or body as having no 
measurable angular motion with respect to the 
fixed stars. We are thus resting firmly on an 
empirical foundation and can expect no argu- 
ments from the philosophers. Absolute rotation 
is now merely relative rotation assessed with 
respect to a fixed direction or a fixed body. With 
few exceptions absolute rotation, or rather the 
rate of absolute rotation, is the subject dealt 
with here. 

The rate of absolute rotation of a line, 
considered either as the total quantity taken 
about an axis normal to the plane of rota- 
tion, or as one of the components of the total 
about some other specified axis, appears as 
an essential variable in lead-computing gun- 
sights, synchronous bombsights, angular rate 
bombsights, rocketsights, stabilizing systems, 
guided missile controls, and so on. As discussed 
in Chapter 1, a prime criterion for the in- 
terception approach is expressible in terms of 
this variable. One of the more spectacular 
applications of the absolute rate of rotation is 
in the principle of low-altitude bombing which 
is discussed more fully in Chapter 7. We wish 
here to signalize the general value of absolute 
angular rate by giving a brief geometrical de- 
scription of this principle. The range solution 
only is demonstrated. 

Consider a bomber flying horizontally over 
a target, at constant speed, and making a 
straight ground track in which the target is 
contained. The direction from the target to the 
bomber is increasing in elevation, whereas that 


from the bomber to the target is dropping in 
angle below the horizon in a precisely corre- 
sponding manner. In terms of the altitude h 
of the bomber, the remaining horizontal dis- 
tance d on the ground track, and the horizontal 
speed V of the bomber in target coordinates, we 
may obtain an expression for the absolute rate 
of rotation w of the sight line from bomber to 
target, as seen from the bomber. We find easily 


vh 

-j- 


( 1 ) 


Now if a given value of w, say wo, is considered, 
we see that the locus of points in which an air- 
plane, flying with relative speed in a vertical 
plane through the target, sees the target mov- 
ing with angular rate wo, is given by 


+ = 


vh 

coo 


( 2 ) 


This is evidently a circle lying in the given 
vertical plane, containing the target as a point 
of its circumference, and having its center pre- 
cisely V 2 V/(Oq above the target. As v and wq 
change, we see that the circular locus merely 
swells or shrinks but still passes through the 
target and is still symmetrically disposed 
above it. 

The locus of release points for a bomb on the 
other hand, for negligible air resistance, is 
merely an inverted trajectory with apex in the 
target. Such a locus is a vertical parabola con- 
taining the target, and may be written, using 
g for the acceleration of gravity, as 


h = 



(3) 


We now choose wq in equation (2) so that the 
circle osculates the parabola, noting that the 
center of the circle, and the apex and focus of 
the parabola, are collinear. Placing the center 
of the circle at the center of curvature of the 


:ONFIDENTfAL 


35 


36 


TECHNOLOGY OF ROTATION IN SPACE 


parabola, referring to the nature of the curve 
at the origin, we have 

V 

2coo g 

It may readily be sho’wn that for typical speeds 
the closeness of the mutually osculating curves 
is remarkably good for altitudes belo'w 500 
feet, and thus that they can replace one another 
there. Thus a bomb may be released when, ap- 
proximately. 


Several refinements must enter before a prac- 
tical sight results, but the inputs other than 
those of equation (4) are of second order im- 
portance. The method is relatively independent 
of altitude at low altitude, for example, and as 
a slightly extended analysis will show is re- 
markably insensitive to a departure from hori- 
zontal flight. A number of bombing applications 
result from this principle, which differ among 
themselves by virtue of the manner in which 
the angular rate criterion is incorporated. 

3 2 ALTERNATIVE METHODS OF 
MEASUREMENT 

The phrases ‘‘rate of rotation in space,” “ab- 
solute rate of rotation,” and “absolute angular 
rate,” are being used interchangeably here. 
When the context leaves no ambiguity, the term 
angular rate itself will frequently be employed 
as equivalent to the above phrases in order to 
simplify the construction of sentences. 

When it is desired to determine, from a ve- 
hicle, the absolute rate of rotation of the direc- 
tion from the vehicle to an external object, one 
has the choice of various instrumental proce- 
dures. It must first be well understood, in any 
given case, what axis or axes it is desired to 
employ as references, or about which the angu- 
lar rate is to be measured. Suppose that a gyro,^ 
in appropriate gimbals, is subjected to torques 
about axes normal to its polar axis, and that 
these torques are so regulated that the polar 
axis of the gyro is made to point directly and 
continuously toward the given external object, 
say the target. If the two axes, about which the 


applied torques occur, are mutually perpen- 
dicular, the torque applied about each of these 
axes measures the component of absolute angu- 
lar rate, of the given direction, about the other 
axis, and the total angular rate in space of the 
given direction may be compounded vectorially 
from these two orthogonal components. The 
sensitivity of the measurement is proportional 
to the moment of momentum of the gyro, and 
consequently to the speed and inertia of the spin- 
ning wheel, both quantities being assumed to be 
so large that the torques corresponding to angu- 
lar acceleration are relatively small. If this is not 
the case, as it usually is, the two angular rates 
may still be extracted, assuming always that the 
target is being perfectly tracked, by a dynamic 
compensation and a mixture of the torques cor- 
responding to the two components. Of course 
when the applied torques are imposed about 
axes which are not normal to the polar axis, as 
is frequently the case in practice, then the ap- 
propriate resolution must be made on to equiva- 
lent axes which are so located. 

Suppose on the other hand that a rigid frame- 
work, mounted in similar gimbals, is so manipu- 
lated by the control of torques with respect to 
the vehicle that a definable direction fixed in the 
framework is also pointed directly and contin- 
ually at the target. This is a rather pure prob- 
lem in servomechanism, with an inertia load, 
aside from the detection itself of the target di- 
rection. If now (absolute) angular rate meters, 
of which several types are to be described be- 
low, are mounted solidly with appropriate 
orientations in the rigid framework which “fol- 
lows” the target, then the indications of these 
meters provide measurements of the absolute 
rate of rotation of the direction to the target 
taken about axes which are determined by the 
orientation of the meters in the framework, of 
the framework in the vehicle, and of the vehicle 
in space. 

Again, assume that the vehicle carries a com- 
pletely stabilized body, possessing no appre- 
ciable absolute angular motion. Assume fur- 
ther that means are available for the continu- 
ous determination of relative angular rate. 
Such means may, for high precision, consist in 
a feedback arrangement whereby angular mo- 
tion is created under the control of a positional 


ALTERNATIVE METHODS OF MEASUREMENT 


37 


null, or of positional error detection. If then an 
index is pointed continuously at the target, 
either through the application of torques, to 
the index member, with respect to the vehicle, 
or with respect to the stabilized body, and the 
above means is employed to measure the angu- 
lar rate components with respect to the sta- 
bilized body, these measurements are also valid 
with respect to space. We mention some prac- 
tical points : 

Usually the direction to a target is capable of 
much slower instantaneous rotation than is the 
vehicle. Thus, if an articulated massive system 
is forced to point toward the target, the torque 
required will be largely used in overcoming the 
friction in the drive between the vehicle and the 
pointing system. This is not true, however, with 
regard to rotation of the pointing system about 
the direction to the target. The precession of a 
gyro, with spin axis as pointing index, to follow 
a target has several advantages. First it is self- 
stabilizing, opposing inherently those inadver- 
tent torques which arise from angular motion 
of the vehicle. Furthermore it provides a more 
naturally stable dynamic system, for a given 
excellence of servo design, leading thus to an 
easier problem in servomechanism. 

Finally there should be mentioned the method 
in which (absolute) angular rate meters are 
used to measure the (absolute) rates of rota- 
tion of the vehicle itself about axes which are 
fixed therein. It is evident that the angular 
velocity of the line in space from the vehicle to 
the target may be compounded from the angu- 
lar rates of that line with respect to the vehicle, 
together with the absolute angular rates of (the 
coordinate system in) the vehicle. The geometry 
involved is not trivial, but is completely delin- 
eated — for example — in Euler's transforma- 
tions for a rigid body. We note that the com- 
plete angular velocity of the vehicle in space 
may be expressed as the vector sum of its abso- 
lute angular rates about any three mutually 
orthogonal axes which may be chosen in the ve- 
hicle. Thus the measurements afforded by three 
rigidly mounted absolute angular rate meters, 
disposed in the vehicle , so that the axis about 
which each is sensitive lies perpendicularly to 
those of the other two, such measurements that 
is, are completely definitive of the angular ve- 


locity of the vehicle in space. If the case is con- 
templated in which the target is seen more or 
less directly ahead of the vehicle, or in which 
the lead angles between target direction and 
vehicle heading are always less than, say, 45 
degrees, then a geometrically simpler situation 
results. Here the system which measures the 
angular rates of the target direction with re- 
spect to the vehicle, the most significant of 
which are typically the time rates of change 
of the lead angles in two coordinates, combines 
naturally with the system for measuring the ab- 
solute angular rates of the vehicle. Thus for ex- 
ample the axes chosen for measurement of the 
latter may be the same as for the former, both 
being stationary in the vehicle. Quite valid ap- 
proximations may be employed to simplify sub- 
stantially the dynamic system which is neces- 
sary. Apparatus of this type is described in 
Section 10.5, where its application to the de- 
velopments in the pilot’s universal sighting sys- 
tems [PUSS] project is described more fully. 

The choice in general among the available 
instrumental methods outlined above depends 
on numerous circumstances. (A number of per- 
mutations are obviously possible among the 
systems referred to.) These include the imme- 
diateness of the basic components, in terms of 
procurement or developmental status, the re- 
quirements of precision, the life expectancy to 
be obtained, the size and weight, and the fiexi- 
bility for subsequent alteration and adapta- 
tion which it may be desirable to incorporate. 
This latter item, in the opinion of the writer, 
is one of the most important and yet appears 
to be the easiest to overlook under the stress 
of emergency research. With regard to abso- 
lute angular rate meters, only those having 
small internal angular displacements are con- 
sidered ; certain unique advantages may be 
claimed for such components. One is the in- 
strumental flexibility which follows from the 
technique of measuring accurately and per- 
manently a fundamentally important quan- 
tity, involving, thus, a component which need 
not change form in dependence on the dy- 
namics or the geometry of the particular prob- 
lem at hand. Another advantage lies in the 
absence of angular discontinuities, or limits of 
predictable motion, which haunt the designer 


38 


TECHNOLOGY OF ROTATION IN SPACE 


of gimbals and bails for certain other angular 
rate components, and which lead to problems 
in locking and in protection against wear dur- 
ing idle intervals. A further advantage lies in 
the avoidance of friction in the measuring as- 
sembly, since, owing to the use of small angular 
displacement, or even of a null system with re- 
gard to such displacement, traditional bearings 
may be replaced by almost completely friction- 
less structures which require no care or main- 
tenance. 

3 3 PRINCIPLE OF THE CAPTIVE GYRO 

By captive gyro is meant a component com- 
prising a balanced rotor, spinning at substan- 
tially constant speed, of which the axis is con- 
strained to remain very close to a fixed index, 
in one or two dimensions, within a supporting 
framework. The operation of constraint has 
been referred^ to as capturing. 

With a captive rotor of this sort, having suf- 
ficiently large moment of momentum, and pre- 
supposing a small angular departure between 
the spin axis and an arbitrarily varying index, 
the total effective torque which is applied to 
the rotor about all axes normal to the spin 
axis of the rotor is a direct measure of that 
angular rate in space of the latter axis, and 
hence very nearly of the varying index. More 
generally, the applied torque is the vector prod- 
uct of the moment of momentum into the pre- 
cession rate, all three physical quantities being 
treated as vectors. Thus approximately 

Lr^ = 7 [r X r ] , (5) 

where the unit vectors r^ and r® point in the 

“Captive gyros have been variously identified in con- 
temporary nomenclature; the name captured gyro may 
have become the most familiar. R. O. Yavne, who ar- 
rived in our laboratories by a devious route after a 
hectic international migration, and of whom this is 
hardly the only (or the best) reminiscence, was assigned 
to the technical development of captured gyros owing 
to his demonstrated facility with recondite dynamics. 
It was not at first understood why he was reluctant to 
work on this phase of research, it being unknown that 
his reluctance stemmed actually out of an imperfect 
grasp of idiomatic laboratory talk, until he finally sum- 
moned up the courage to say that he felt it to be a 
disgrace that we couldn’t design our own gyros from 
fundamental principles, rather than to accept as a 
starting point a piece of equipment of enemy origin 
which had fallen into our hands ! 


direction of the torque and spin axes respec- 
tively, and where it is to be noted that f® is 
simply the vectorial precession rate in space. 
The amplitude of f® is the scalar precession 
rate w, which is thus measured by the scalar 
torque L under the circumstances above named, 
since further the rotor speed n and its spin 
inertia I may be held constant. 

Equation (1) describes the relation between 
precession and applied torque for a gyro 
whether or not the technique of capturing is 
to be used, and of course only holds when the 
acceleration torques are assumed negligible. In 
the captive gyro r® is to be held close to some 
direction fixed in a supporting framework, and 
r^ is so arranged as to be restricted to direc- 
tions normal to the first direction. In what we 
may call a captive gyro of the first kind, the 
spin axis r® is allowed to rotate, however little, 
in one plane only in the framework; this plane 
ordinarily contains the spin axis and is normal 
to a second axis of rotation fixed in the frame- 
work, imposed, for example, by a single gimbal 
or by bearings between the framework and the 
nonspinning case of the rotor. Rotation of the 
spin axis in the 'Tree” plane within the frame- 
work is opposed by a torque, applied about the 
above second axis, which depends on the rela- 
tive displacement in one dimension of the spin 
axis from the fixed or index direction in the 
framework, and which operates to keep this 
relative displacement to a minimum. The ap- 
plied torque thus measures the absolute angu- 
lar rate of the spin axis, and consequently 
to a high approximation of the fixed index, 
about an axis fixed in the framework and nor- 
mal both to the fixed index and the above sec- 
ond axis. The approximation improves in pro- 
portion to the closeness with which the dis- 
placement referred to is held near zero. In 
order that the total applied torque may be 
principally contributed by a measurable or re- 
producible agency, it is essential that the fric- 
tion involved in the rotation of the gyro about 
the second axis, the precession axis that is, be 
made insignificant in comparison with the re- 
storing torque which corresponds to the small- 
est angular rate to be detected. 

Most of the captive gyros we have dealt with 
have been of the first kind. A single gimbal 


PRINCIPLE OF THE CAPTIVE GYRO 


39 


axis only has been involved, and a single scalar 
reading has thus been provided for the abso- 
lute angular rate of the framework about a 
fixed line therein. Such a component, when 
adequately fast and accurate in response, may 
serve as a basic element to be used singly or 
in sets of two or three, being mounted in ap- 
propriate positions in a vehicle or in an artic- 
ulated body, and has many diverse applica- 
tions in aiming controls. A few remarks, to 
turn to the practical side for a moment, are 
warranted on the available methods for driving 
the rotor. The methods we have been concerned 
with divide first into pneumatic and electric, 
the electric methods split further into d-c and 
a-c, and a-c types are either synchronous or 
nonsynchronous. Alternating current drives 
are commonly either two-phase or three-phase. 
Of the pneumatic method, which is economi- 
cally feasible only if associated pneumatic 
equipment is involved, we may say that speed 
regulation for the rotor has as yet only been 
experimentally worked out. Such work has been 
largely carried out by Section 7.3 and has in- 
volved both a resonant reaction to the periodic 
impingement of the driving jet on the cups of 
the rotor (the reaction throttling the jet flow) 
and a centrifugal brake, although several 
other arrangements have at least been pro- 
posed. In rotor drives involving direct current 
motors, one advantage is the simplicity of 
speed regulation, but a disadvantage is ap- 
parent in the problem of brush wear, which 
may unbalance the gyro by moving the cen- 
ter of gravity along the spin axis. This is a 
very real consideration, where the instrument 
is to have an appreciable operating life, since 
unbalance of this sort will give a false measure- 
ment of angular rate in dependence on the 
acceleration of the vehicle or platform. It is 
claimed, however, that such motors, or rather 
combinations of such motors and gyro wheels, 
can be made in which the abraded brush or 
commutator material will fly out radially and 
stick permanently at the original distance from 
the precession axis. The writer has not had 
sufficient opportunity to test this claim. In the 
employment of synchronous motors which 
^Hock in^’ at the driving frequency, as with the 
General Electric hysteresis gyro unit, either 


frequency control of an inverter or speed con- 
trol of a motor-generator is essential. In one 
case however, and the following method would 
apply for nonsynchronous drives if the rotor 
frequency is extracted, the response of a cap- 
tive gyro of varying speed was corrected by 
the interposition of a filter in the output which 
altered the overall sensitivity in inverse pro- 
portion to an impressed frequency, the latter 
frequency being made proportional to the rotor 
speed. 

An advantage in captive gyros generally is 
in the avoidance of intricate problems con- 
nected with carrying in power conductors 
through gimbal connections to spin the rotor. 
Owing to the small relative motion of the rotor 
axis with respect to the support, flexible con- 
nections are possible if care is taken to avoid 
fortuitous spring-torques. In the pneumatic 
case, as in the partially captive turn gyro of 
familiar renown, a nozzle fixed in the support- 
ing case is adequate if aerodynamic symmetry 
is preserved. 

Very briefly, the techniques for capturing 
and for torque measurement, in captive gyros 
of the first kind, are as follows. First, one 
may constrain mechanically the relative rota- 
tion of the spin axis, in its attempt to process, 
and then may measure the small angular de- 
flection which results and which is propor- 
tional to the constraining torque, provided of 
course that appreciable friction is not also con- 
tributing to the constraint. The requirements 
for high accuracy are: high undamped fre- 
quency of the oscillatory mechanical system, 
predictability of the resilient member, negli- 
gible drift of the zero position with temperature 
and time, means for accurate measurement of 
the small displacement, and enough damping 
to give rapid decay, on the time axis, of tran- 
sient excitations. Symmetrical oscillations of 
high frequency are usually harmless since 
these are ignored by the subsequent compo- 
nents into which the output is fed, but random 
disturbances, which have a propensity for con- 
taining energy in the lower-frequency band, are 
meticulously to be guarded against. Such dis- 
turbances, which establish a threshold in detec- 
tion, may arise, for example, from the shock 
impulses and noise in imperfect rotor bearings. 



40 


TECHNOLOGY OF ROTATION IN SPACE 


The second method principally in use in- 
volves a feedback loop whereby the error or 
unbalance in angular displacement of the spin 
axis with respect to the framework initiates 
application of a torque so related dynamically 
to the error that the latter is reduced to small 
magnitude and maintained there. The applied 
torque then measures the angular rate which 
necessitated it. Such an arrangement may or 
may not have an added resilient system which 
applies an unmeasured torque in proportion to 
the error or to its rate of change. Even in the 
presence of such resilient or viscous attach- 
ments, the feedback method operates substan- 
tially without error from such sources if a 
small and properly located null is maintained. 

The problem of the two-dimensional captive 
gyro, of the second kind, as we may say, is 
rather different. In the first place the need for 
a double gimbal, to permit rotation of the spin 
axis about a point instead of an axis in the 
framework, leads to a more difficult balancing 
problem about the two processional axes which 
must then be considered. Furthermore, as is 
well known, a gyro resiliently restrained in 
two dimensions will nutate violently if afforded 
the slightest opportunity. Even with zero con- 
straint, the so-called free gyro will nutate for- 
ever in the absence of bearing friction or other 
losses. The principal obstacle is overcome, how- 
ever, when the danger of nutation is recognized 
and provided against. Again there are two dis- 
tinct capturing techniques, as above, and al- 
though they do not involve simply a duplicate 
application of the one-dimensional techniques 
for each of the two processional axes, success- 
ful controls have been worked out which com- 
pensate for rotational tendencies. 

The gain in captive gyros of the second kind, 
over those of the first kind, is particularly ap- 
parent only when two of the latter are replace- 
able by one of the former. Where three inde- 
pendent angular rates are desired it is almost 
preferable to use three of the simpler units 
owing to the resulting similarity of the basic 
units. 

3 4 GYROS FOR ANGULAR RATE BOMBING 

The development of angular rate bombsights 
as such, with a description of their place in 


the larger field of airborne aiming controls, is 
dealt with in Chapters 7 and 10. Here we shall 
discuss the research effort which revolved 
around the design of captive gyro components 
for such bombsights, beginning with those for 
the original hand-held BARB, which incorpo- 
rated the theoretical principle of British-type 
angular rate bombing for low-altitude attacks. 

Requiring a method for measuring the abso- 
lute rate of rotation of a framework which 
was turned about a substantially horizontal 
axis, and there being reason to desire an accu- 
rate, sensitive, and reproducible such measure- 
ment, the application was naturally considered 
of a captive gyro of the first kind, as above 
identified. For this and similar applications it 
was proposed originally by the writer (al- 
though similar proposals may have been made 
elsewhere) to construct a captive gyro of the 
first kind having extremely stiff mechanical 
constraint and to measure angular rate as 
strain through the response of wire-type strain 
gauges on the constraining members. This was 
essentially a nonfeedback proposal, the ap- 
proximate null in angular displacement not 
being “sought’' by retroaction but being as- 
sured through the relatively high stiffness of 
the constraint. It was considered that strain 
gauges of the type suggested would enable 
measurement of the gyro torque, and hence of 
angular rate, in terms of the small strain (or 
small dimensional changes) thereby produced 
in the members. Such gauges were known to 
respond measurably to fractional strains of the 
order of one part in a million, and to yield 
changes of resistance in extremely rapid and 
faithful correspondence with the dimensional 
alterations of the structure to which they were 
attached. The techniques of balancing out (by 
the employment of bridges, etc.) the errors 
owing to the temperature coefficient of the 
gauge wires was quite well understood, but it 
was not at first suspected what extreme care 
was necessary to guard against drift which 
arose from humidity variation. Nor was the 
difficult problem of noise completely foreseen. 
It was recognized at an early stage, however, 
that a very great advantage followed from the 
general arrangement suggested, in that no or- 
thodox bearings need be involved, and hence 


GYROS FOR ANGULAR RATE BOMBING 


41 


no sliding or rolling friction. Friction is the 
deadly enemy of torque measurements, whether 
these are to be obtained through deflection or 
through a feedback balancing of forces. 

Half a dozen models of such captive gyros 
were built including one or two of the second 
kind, all involving the strain gauge technique. 
Experimental constraining members in a great 
variety of forms and shapes were tried out, 
with various dispositions of the gauge ele- 
ments*’ on them. Combinations of single and 
double cantilevers were at first most popular, 
although somewhat later cylindrical members 
came into vogue in the laboratory. One exam- 
ple of the latter sort involved a pair of thin 
bronze cylinders placed in a line coaxially, with 
the gyro connected between them so that its 
spin axis was coincident with the cylinder axes 
and its case rigidly connected to the two cyl- 
inders at their inner ends. The outer ends of 
the cylinders were rigidly connected to a sup- 
porting framework. Gauges were applied sym- 
metrically, four to each cylinder, and oriented 
along the elements thereof. Although the con- 
straining members supported the gyro and its 
case against accelerations, such as that of 
gravity, with a corresponding deflection of the 
elastic constraining structure, such deflection 
was always “even” and was not measured by 
the bridge system in which the several gauges 
were connected. “Odd” deflections, correspond- 
ing to the angular rate torques, were measured 
by the system in terms of the differential re- 
sistance change of the gauges. A rather care- 
ful elastic analysis was made of the mechani- 
cal system which was fundamental to this ar- 
rangement, and corroboration was experimen- 
tally found to a satisfactory approximation. 

The difficulties which were experienced with 
the above absolute angular rate meter were 
typical of those found in the case of other 
meters in which strain gauges were used. We 
have already mentioned the variation in gyro 
speed and the attempts to compensate for it 
after the fact, as in the eddy-current dome of 

’’On the practical problems which arise with regard 
to the application of these elements, The Foxboro Com- 
pany and Ruge-deForest were consulted freely and at 
some length. The gauges themselves and certain 
auxiliary calibrating equipment were obtained also 
from these sources. 


a disturbed sight, so called, but although some of 
these attempts were ingenious (such as in the 
excitation of the a-c measuring bridge by a mag- 
netic system on the gyro rotor, and the insertion 
of filters of transmission inversely sensitive to 
frequency) , we shall not treat them further since 
similar problems are common to other types of 
gyroscopic rate meters, except to say that speed 
regulation is a comforting feature to plan on for 
the rotor. The problem of drift in the gauges 
themselves, to say nothing of drift in the attend- 
ant circuits, is a straightforward one ; there are 
now, it is understood, standard procedures 
whereby this problem is surmountable in other 
strain-measuring applications. It may be noted in 
passing that the commoner role of the wire- 
type strain gauge is in strictly dynamic mea- 
surements, where the long-term maintenance of 
a zero indication is less important than in the 
case here discussed. 

The most refractory problem was the un- 
wanted response of the gauges to noise origi- 
nating in the bearings of the gyro rotor. No 
trouble was found owing to vibrations arising 
from unbalance of the rotor, the reason pre- 
sumably being that the deflections resulting 
were symmetrical and principally of a single 
fundamental frequency with a predictable har- 
monic content. With these circumstances, how- 
ever, the rotor bearing disturbances have noth- 
ing in common. They are random and hence 
symmetrical only over an appreciable time in- 
terval, and further contain frequencies over 
the whole band. For the bearings with which 
we were dealing, the noise signals were such 
as to give a threshold which was appreciable 
in comparison with the smallest angular rate 
signals desired. In a d-c system, an obvious 
measure would have been to lag the response 
until the resulting statistical processes gave a 
final measurement not biased by the fortuitous 
disturbance, and to accept the lower perform- 
ance in promptness of response. With the a-c 
measurements which were being tried at that 
time, however, a good deal of trouble was given 
from this source in the phasing adjustments 
involved in polarity sensing. Of course the 
cleanest cure is to improve the bearings, and 
certain modern gyros are of an order of mag- 
nitude better in respect to noise, even for cor- 


.GONFIDENTIALI 


42 


TECHNOLOGY OF ROTATION IN SPACE 


responding sizes. (Larger gyros, in which pro- 
cessional torques are relatively bigger in com- 
parison with the bearing noises, are less trou- 
blesome in this respect.) 

Several other methods were considered, how- 
ever, for the avoidance of this evil, but were 
never tried out. One such was the proposal to 
add elastic members which responded identi- 
cally to the vibrational disturbances trans- 
mitted from the gyro bearings, being associated 
with the gyro case in the same way as were 
the normal members, but which were not 
stressed by the precessional torques, owing to 
the fact that they were not also to be connected 
to the framework. Then, of course, the dif- 
ference in indication by gauges attached to 
both kinds of members would be extracted. Al- 
though some very delicate questions would 
arise, in this connection, on the detailed dy- 
namics of such a measure, it is still felt that 
thereby an appreciable improvement might 
have been obtained. A good many planned ex- 
tensions of this sort were discarded when the 
pneumatically captured gyro appeared (to be 
mentioned again below) and it is difficult to 
guess what success ultimately might have been 
attained. As it was, the captive gyros which 
were developed were almost adequate for the 
bombing application at hand. Most of the fail- 
ures in test were actually in circuital com- 
ponents rather than in the gyro structures or 
the gauge mountings. 

We should add that the angular rate bomb- 
sight was not the only aiming control system 
for which captive gyros were designed as ab- 
solute angular rate meters. The most impor- 
tant application, probably, with which we 
have been intimately concerned has been as 
an input component for the PUSS system, 
which is described elsewhere. There the cap- 
tive gyros are used to measure the angular 
rates of the airplane about its own axes. Other 
applications included one in which extremely 
small absolute rates were to be determined, for 
use in a secondary control for refining the ex- 
cellence of a precision vertical. Proposals have 
also been made for the use of captive gyros, of 
the sort here treated, in guided missiles, sta- 
bilizing systems, for internal torpedo controls, 
and for gyro compasses. 


Nor should we give the impression that the 
wire-type strain gauge was the only tool em- 
ployed to measure the small deflections of cap- 
tive gyros in which feedback was omitted. 
Such other responding agencies as E magnets 
and autosyns were also given a chance at this 
job, and one of the most promising alternative 
approaches involved electromagnetic detection 
of the deflection of a small magnet spinning on 
the axis of the gyro rotor, the rotor and case 
being flexibly mounted to permit small elastic 
rotation. An endearing property of this trick,<^ 
which was discarded for other reasons, was the 
very great sensitivity to small angular rates 
of which it was capable. 

All of the detection methods, by which an- 
gular displacement is tangibly extracted in the 
nonfeedback captive gyro, are applicable as 
error detectors or unbalance detectors in terms 
of relative motion when feedback is employed. 
This application naturally requires less ideally 
characterized response in the detecting means, 
since the approximate maintenance of a null 
is all that is asked for. The accuracy of mea- 
surement is afforded by the known characteris- 
tics which obtain between some other physical 
agency and the balancing torque. Errors aris- 
ing at intermediate points may be annihilated 
through the ultimate comparison of the output 
with the input precessional torque itself. It is 
not necessary to enumerate the many advan- 
tages which follow from the feedback tech- 
nique. The only disadvantages lie in the possi- 
bility of greater complexity and in special 
problems required for the maintenance of sta- 
bility, not only at any given time but through- 
out the useful life of the equipment. 

A very compact feedback arrangement was 
embodied in the pneumatic captive gyro which 
ultimately replaced the electric forms in the 
angular rate bombing problem. This develop- 
ment was conducted almost entirely by Section 
7.3, working in collaboration with Section 7.2, 
and thus need not be described in detail here. 
(See Volume 1, Chapter 4.) The capturing 
method led to a maximum relative angular dis- 
placement of the order of a milliradian, and 
consisted in a valving process, with the gyro 

'Attributable to W. Sheppard of The Franklin In- 
stitute. 



A PARTICULAR CAPTIVE GYRO OF THE SECOND KIND 


43 


and case serving as the sole moving part, 
whereby pressure areas were enabled rapidly 
to balance the precessive torque and maintain 
the displacement null stably and to within close 
limits. The pressure difference between the 
valved pressure areas indicated the angular 
rate as output. It was found necessary to damp 
the motion of the moving system, and, although 
several equivalent pneumatic methods were 
proposed, a rotary dashpot with viscous fluid 
proved most successful practically. No attempt 
was made to prepare a captive gyro of the sec- 
ond kind by this technique, although it was 
generally recognized that this would have been 
possible. The mechanism employed appeared 
simple and effective, but there is reasonable 
assurance that a number of drastic variations 
would serve as well. 

In the most modern of the pneumatic captive 
gyros, now being considered for the pneumatic 
form of PUSS, crossed-spring flexures have re- 
placed the gimbal bearings. Earlier experi- 
ments indicated that with such flexures and 
with the pneumatic-capturing technique, no 
lower limit for the detectable angular rates 
was evident. 

3 5 A PARTICULAR CAPTIVE GYRO OF THE 
SECOND KIND 

As a basic component of the pilot’s universal 
sighting system, the project for the prepara- 
tion of which is discussed in detail in Chapter 
10, and for the provision in that system of in- 
put data comprising the instantaneous angu- 
lar rates of the airplane about its own vertical 
and lateral axes, one of the units which was 
proposed and developed was built around the 
gyro element constructed by GE for a sight 
stabilizer in one form of flexible gunnery di- 
rector in the Superfortress. This gyro element 
involved an asymmetrically mounted rotor and 
motor in a double gimbal system of small 
dimensions. E magnets detected the deflections 
of the gimballed system in two dimensions, and 
pancake coils mounted at right angles on that 
system moved in a magnetic circuit stationary 
on the frame. Currents were supplied through 
flexible leads to each of these coils and to the 
d-c gyro motor, which was locally speed-regu- 


lated. Tuned, frictional, nutation dampers had 
been supplied for the original function of the 
unit, which was as follows. In tracking, an 
operator supplied currents from his handle- 
bars, through dynamics which imposed “aided” 
performance, to the pancake coils on the gyro. 
These currents precessed the gyro axis over a 
two-dimensional fleld in rapid response to the 
manipulations of the operator, providing, inci- 
dentally, a fundamentally stabilized system. 
Then the whole sighting platform, on which 
the gyro element was mounted, was made to 
follow the gyro axis by appropriate servo- 
mechanism. The rest of the Are control equip- 
ment was of the nature, more or less, of a 
standard director, use being made of the 
precessing currents in the pancake coils as 
measures of angular rate. 

It was proposed by the writer to employ this 
same gyro element, for our application, quite 
the other way around, but thereby to use al- 
most all the features of this existing develop- 
ment. First, the mounting or framework of the 
gyro element was to be flxed in the airplane in 
such a way that the neutral direction of the 
gyro axis pointed along the longitudinal axis 
of the airplane. Then, under arbitrary motion 
of the latter, the currents in the pancake coils 
were to be manipulated automatically to 
process the gyro axis continually into coinci- 
dence with its neutral direction in the frame- 
work and hence into coincidence with the lon- 
gitudinal axis of the airplane. Since the ap- 
plied currents would also accelerate the mass 
of the gyro rotor, together with the motor and 
the gimbals, means must be provided, in the 
regulating channels, to separate the conflict- 
ing accelerating and precessing tendencies, and 
to achieve stability in the null-seeking process. 
As before, the currents in the pancake coils 
were to be used as direct measures of the in- 
stantaneous angular rates. 

During the course of the development which 
followed, and which resulted in the attainment 
of reasonably good success in terms of the 
characteristics sought, it was found best to 
dispense with the existing nutation dampers. 
By following the differential equations which 
were prepared, a logical sequence of control 
design proved feasible, being capable of cor- 




44 


TECHNOLOGY OF ROTATION IN SPACE 


roboration at every point, which led to con- 
firmation of the degree of precision and sta- 
bility indicated by the analysis. We were look- 
ing for time constants in the response of the 
order of 0.2 second. These were attained or 
exceeded. We wanted a reliable measurement 
of angular rate from a resolution of 0.0005 
radian per second up to a maximum indica- 
tion of 0.30 radian per second. We obtained 
such performance from 0.0003 up to 0.50 ra- 
dian per second. This development continues, 
owing to its application in projects of Navy 
interest, the current work concerning chiefly 
the engineering design of the electronic con- 
trol channels. It is evident, incidentally, that 
precise regulation of the electrical supplies to 
the latter channels is unimportant. 

A word more on design details and testing 
methods. The general control connections were 
from each E magnet “around the corner” to 
the coil which produced the corresponding 
precession. A pair of cross connections, with 
the appropriate operational characteristics, 
compensated for the inertia coupling which 
otherwise would unstabilize the mutual opera- 
tion of the two modes of control which were 
simultaneously present. Since the E magnet 
indications were at 400 cycles per second, 
phase reference and rectification were neces- 
sary in each channel, the dynamic networks 
and the final currents being preferably at di- 
rect current. Thyratrons were finally used, for 
space economy, to supply these final currents. 
With milliammeters in the output current 
leads, and with the gyro axis under automatic 
close capturing and the framework either hand- 
held or on a turntable, an impressive demon- 
stration of rapid, sensitive, and accurate angu- 
lar rate measurement was available, and was 
seen by many visitors. Remaining small fluc- 
tuations in the gyro axis, and correspondingly 
in the output currents, are of magnitude con- 
sonant with the resolution of measurement; 
these are now considered to be traceable, not to 
mechanical friction in the gimbal bearings (ap- 
proximately 0.001 inch-ounce) but either to 
rotor bearing noise — as above — or to torque 
impulses applied nearly about the spin axis by 
the d-c regulator of the driving motor. 

Short of very completely instrumented (and 


ultimately essential) trials in the air, there are 
several good methods for testing angular rate 
meters in the laboratory. Although turntables 
are a problem in themselves, which we shall 
not here discuss, and are difficult to accelerate 
rapidly and predictably, a very convenient 
method for imposing and removing pseudo-rates 
in space is merely to add weights on the hori- 
zontally disposed axis of the gyro. 

^ ^ A CAPTIVE GYRO WITH CAPACITIVE 
DEFLECTION DETECTION 

One of the more recent endeavors in captive 
gyros for absolute angular rate measurement, 
within our group, has involved a return to the 
nonfeedback method. Given a smoothly running 
constant speed gyro in a case, and a method 
of predictable and frictionless constraint, a 
very powerful means for the measurement of 
mechanical displacement is provided by the 
variation of electrical capacitance between ad- 
jacent parts which belong respectively to the 
gyro and to the framework. The compensation 
for those displacements which it is desired not 
to measure may thus be made inherent, rather 
than through the subsequent response to a dif- 
ference between two appreciable quantities. 

The use of capacitive methods may become 
quite appropriate when a number of such meas- 
urements or computations may occur through- 
out the system, so that a common oscillator 
will serve. The advantages of these methods 
are many, and they include low reaction on the 
measured structures, precision telemetering 
without local follow-up devices, and the oppor- 
tunity for employing capacitive “slip-rings,” 
of higher capacitance than, and in series with, 
the measuring capacitor. The latter may thus 
be placed in an electrically remote position in 
a mechanical system. 

In the experimental apparatus referred to 
here, the gyro, which has been initially one of 
the first kind and may later be generalized, 
was mounted entirely on four leaf-flexures. The 
flexures were mounted radially, fastened along 
their inner edges rigidly to the gyro case and 
along their outer edges to the frame, and 
were so disposed that their common intersec- 
tion (if each flexure were imagined to be cen- 


AN OSCILLATORY CAPTIVE GYRO 


45 


trally extended) intersects and is normal to 
the gyro axis. The gyro axis is thus allowed 
to deflect principally, although very little, about 
the common intersection of the flexures as 
precession axis. On rigid members moving with 
the gyro case, and extending perpendicularly 
to the above precession axis, are mounted ca- 
pacitor plates at the outer ends. Mate plates 
are attached to the frame, at each end and on 
each side, providing two pairs of series capaci- 
tors which, placed in a bridge, respond solely 
to deflections which arise from precessive 
torque. For the problem at hand, the response 
to angular acceleration is negligible in com- 
parison. A gyro of about 2 inch-pound-seconds 
is now being used, and it is planned to allow 
about 0.002 radian of relative angular displace- 
ment at maximum. An individual capacitance 
of 10 micro-microfarads is being contemplated, 
which may have a total variation of 20 per 
cent. Computations indicate a resolution well 
below 0.0001 radian per second, and a time 
constant less than 0.02 second. This develop- 
ment is still in progress and may be continued 
by BuOrd through a separate contract (NOrd 
9644) extending the work now under Project 
NO-265. 

3 7 AN OSCILLATORY CAPTIVE GYRO 

Suppose, in a captive gyro for absolute an- 
gular rate determinations, that the rotor turns 
t)eriodically, first in one sense and then in the 
other. If under these circumstances the polarity 
of the angular rate measurement also were al- 
ternately reversed, in synchrony with the re- 
versals of rotor spin, the measurement of an- 
gular rate might be altogether unaffected. This 
indicates the attractive possibility, which oc- 
curred to the writer some time ago, that a 
captive gyro might be built without conven- 
tional rotor bearings. 

If the rotor were oscillated about an axis 
therein, say with perfect harmonic motion in 
angle, then it might be connected to the frame- 
work by flexure-bearings, serving themselves 
as resilient means which would allow preces- 
sive deflection. For an angular rate in one 
direction, with respect to space, the precessive 
deflection would also be oscillatory and of the 


same frequency as that of the rotor. The am- 
plitude of the precessive oscillation would in- 
dicate amplitude of absolute angular rate, and 
its phase with respect to the rotor oscillations 
could presumably determine the sign of the an- 
gular rate. A resonant drive for the rotor seems 
not impossible, and the precessive mode might 
also be somewhere near resonance to give an 
increased response. Such arrangements would 
be limited by the phase relations of the me- 
chanical coupling. Systems of strain gauges 
could be mounted on the flexing members, and 
bridge-connected in various obvious ways to 
ignore or to detect the several deflections and 
the corresponding torques, and hence to meas- 
ure angular rates. 

As to frequency, the higher the better, on 
the whole, but note that the flexural accelera- 
tions and the centrifugal stresses increase with 
the square of frequency, whereas the peak mo- 
ment of momentum increases only linearly 
therewith. When the frequency is increased, 
for a given rotor, altering the amplitude to 
keep the energy content similar to that in a 
standard nonoscillating gyro, it may be shown** 
that rupturing stresses for any conceivable ro- 
tor shape or substance are reached at fairly 
low frequencies (such as 25 cycles per second). 
Now it may not be essential to maintain a 
high energy content, since ultimately angular 
deflection only is sought, and friction should be 
almost completely absent. Thus, in accord with 
the dimensional relations well known to 
strength of materials engineers, a very small, 
high-frequency gyro oscillator might turn out 
to be practical. This is even more attractive, 
since then the whole unit might be sealed up 
in vacuo, there being no bearings or other main- 
tenance needs, much as with a vacuum tube. 
It is apparent that the measuring system might 
be the limiting feature, at least for the wire- 
type strain gauges, but there is no fundamental 
reason why such other means as capacitor 
gauges, where reasonably high frequencies 
might be locally at hand in the resonant drive, 
or even electronic or ionic detecting elements, 
might not work out. Since the direct measure- 

‘*This whole question was discussed with W. H. Howe, 
Research Director of The Foxboro Co., and some of 
the considerations here expressed are due to him. 


■ CdNFlDENf 


46 


TECHNOLOGY OF ROTATION IN SPACE 


merit of absolute angular rate appears as such 
a universal need in modern aiming controls, 
and more generally yet for high performance 
navigation, it might well be equitable to under- 
write an advanced development of this sort. 

Since the earlier discussions of this proposal, 
we have heard that somewhat similar experi- 
mental attempts, here and abroad, have met 
at least with partial success. For our part, we 
have done as yet no experimental work on this 
topic whatever. 

3 8 CENTRIFUGAL TENSION AS A 
CRITERION FOR MEASUREMENT 

The centrifugal governor responds to rota- 
tional speed with respect to the foundations 
of a machine. This does not generally annoy 
the user, since the rotation of the foundation, 
or rather of the earth, in space is relatively so 
small. However, if such a governor controlled 
the speed of an alternator and were exclusively 
relied on to maintain the accuracy of clocks, 
a given installation, if it made clocks keep 
time at the equator, would run them fast in 
one polar hemisphere and slow in the other. 

Whereas the forces on a single point mass 
depend on linear acceleration and gravity as 
well as on purely centrifugal effects, the fol- 
lowing arrangement will isolate rotation as 
such. Imagine a pair of equal masses joined by 
a weightless and inflexible rod. Neglect the in- 
significant gravitational attraction between 
them. It is not difficult, then, to demonstrate 
that the total tension / in the rod, reflecting the 
mutual separative effort of the masses, will 
be proportional to the square of the absolute 
rate w at which the connecting line rotates in 
space. It will also be proportional to the mag- 
nitude m of either mass and to the distance a 
— assumed constant or very slowly changing — 
between the centers of gravity. Actually, in 
consistent units, 

f = 

It is evident on the one hand that this tension 
can never be negative, and that consequently 
one cannot thus distinguish between rotation 
in a given sense and rotation in the opposite 
sense. We are dealing with a signless affair. 


Furthermore the entire angular rate, in the 
sense of Chapter 1, is measured, the system be- 
having like a captive gyro of the second kind 
in which the only available reading is that 
given by the sum of the squares of the two 
orthogonal angular rate determinations. Com- 
ponents of angular rate cannot be extracted 
directly. This feature is a drawback for cer- 
tain applications, where, for example, the axis 
of the meter is used to track a given arbitrary 
direction, and owing to imperfections always 
present in the tracking operation the axis exe- 
cutes minute wanderings out of the principal 
tracking plane. In such a case the mass-pair 
meter would read high owing to the instanta- 
neous and inseparable contribution from the 
perpendicular mode. For other conceivable ap- 
plications, however, this property might con- 
stitute an advantage. 

The chief disadvantage of the proposed mass- 
pair absolute angular rate meter is that its 
sensitivity drops off very rapidly for slow 
rotation. Thus 0.001 pound would be obtained, 
with one-pound weights one foot apart, for 
an angular rate of about 10 degrees per second. 
This is easily measurable. However, for 1 
milliradian per second, which is significant in 
many branches of fire control, only about 
0.00000003 pound is exerted (10 micrograms 
or so). This is best measured in the laboratory, 
at least under present day circumstances. 

Of the several methods which were consid- 
ered for instrumental utilization of this prin-i 
ciple, only two were mentioned more than once 
or twice. One of these involved a pneumatic 
capturing system involving ten pressure cups 
and a pneumatic double bridge whereby the 
difference between two pressure differences 
could be handled. While probably feasible, the 
extreme requirements on precision of machin- 
ing and adjustment, and the care which would 
have been essential in guarding against tem- 
perature gradients in such a component, ap- 
peared to prohibit the expenditure of time and 
effort. Another method, employing specially 
fabricated flexures and capacitive detection, 
was thought to be practical from the stand- 
point of machining, but the temperature prob- 
lem would have been equally difficult and many 
second order electrical effects would have en- 


gonfidentia: 


POSSIBILITIES FOR THE FUTURE 


47 


tered into consideration. Furthermore, the bal- 
ancing of the mechanical characteristics among 
the several flexure supports would have been 
critical in the extreme. No actual work was 
done on this type of meter beyond analyses 
and computations. The only real appeal lay in 
the essentially motionless nature of the physi- 
cal arrangement, without spinning parts or 
rotating fields. 

If such a general proposal is ever considered 
again, and it may be because it is fundamental 
(we refer to centrifugal tension rather than 
any particular mechanism), it may be worth 
while to consider a feedback from current to 
magnetic force, employing the square law be- 
tween current and flux. The current might then 
respond approximately linearly to the absolute 
angular rate. 

3 9 POSSIBILITIES FOR THE FUTURE 

As has been pointed out above, there ap- 
pears to be great likelihood that the captive 
type of rate meter will come into widespread 
use for many purposes formerly filled by free 
or semi-free gyros. This likelihood is deduced 
from the advantages in flexibility, and the in- 
herent opportunities for improvement which 
have been mentioned above. The tendency also 
should be toward "‘tighter” capturing proce- 
dures. Even now a good, standard, absolute 
angular rate meter of reliable and high per- 
formance would probably find an easy market. 
A further indication is that such meters can 
decrease impressively in size. 

A somewhat different kind of prognostica- 
tion along these lines is that angular accelera- 
tion will find more extensive application as a 
fundamental input. Although (absolute) angu- 
lar accelerometers are not common components, 
such instruments may be constructed to ex- 
tremely high sensitivity, speed of response, and 
tenacity to calibration by modem methods. 


Similar remarks may be made on linear ac- 
celerometers, although these are better known 
and are already considered essential compo- 
ponents in certain important aiming controls. 

In the typical stabilizing device, the auto- 
matic control of acceleration to zero would 
serve as well as that of angular rate, if the 
control were sufficiently delicate and of the 
proper dynamic characteristic, and where the 
regime of control is continuous. This is true 
since either general type of device must use 
long-term guides based on such available land- 
marks as North and Down, however diffi- 
cult it may be instantaneously to fix these latter 
directions. Witness the directional gyro used 
by the pilot. Now we do not recommend that 
this instrument, for example, be replaced by 
an acceleration-controlled body, but indicate 
only that for more complex structures, where 
servomechanisms abound anyhow, the angular 
accelerometer would be at least as good as the 
free gyro or rate meter as a fundamental com- 
ponent. And ultimately it could be smaller and 
cheaper. For control terms, integrations of the 
acceleration may be performed when desired, 
and for this purpose the operations may be 
approximate. Precision integration of absolute 
angular acceleration, for more elaborate pur- 
poses, depends of course on a practical inte- 
grator, which will certainly come but is not 
now generally available. Again, similar remarks 
apply to linear acceleration. Note that the cen- 
trifugal angular rate meter of the last section 
may be considered a differential type of linear 
accelerometer. 

The important feature of absolute accelera- 
tion, whether of angular or linear motion, as a 
fundamental measurable, is its universal avail- 
ability in pure form. Fundamentally, this is 
attributable to the almost perfect constancy of 
the property of inertia (both ordinary and ro- 
tational) in available physical bodies, and to 
the basic measurability of force and torque. 


lONFIDENTI^ 


Chapter 4 


SIMULATION AS AN AID IN DEVELOPMENT 


41 THE PHILOSOPHY OF MODELS 

S O MUCH has been written on the applicability 
and on the potentialities in general of phys- 
ical models that it is hardly proper for the 
writer to give here a comprehensive exposition 
of such techniques, although it should be added 
that he would not find it difficult to articulate 
his enthusiasms for this extremely broad 
branch of technical theory and practice. 

Although in this chapter the methods of elec- 
tronic models, or simulators, are principally to 
be described, model building and model manip- 
ulation range over almost all physical media. 
From one standpoint, most mathematical ma- 
chinery may be considered a class of such 
models, since there must be embodied therein 
a physical system obedient to the same laws 
which apply in the case of whatever other sys- 
tems the machinery is employed to study. The 
differential analyzer, in this sense, and we refer 
to the now familiar form of this weapon, may 
be thought of as a synthesizer, or flexible model, 
as well as an analyzer. This question of names 
is a controversial issue, involving definitions 
rather than anything more fundamental, and 
is most happily resolved by recognition that 
the equipment under discussion is really a 
bridge between analysis and synthesis, bring- 
ing these two essential modes of study into 
closer collaboration. Specific models are more 
prevalent, wherein problems of a particular 
category only may be studied. These may be 
simple replicas of other physical systems, re- 
taining even the geometry and the appearance 
thereof, but by a transformation of one or more 
of the coordinates, of space, time, energy and 
so on, yielding a means for experimentation in 
which certain limitations are removed in com- 
parison with the original systems. The well- 
known principles of similitude and dimensional 
anaylsis are guides for the construction, opera- 
tion, and interpretation of models of this sort. 
In fact the so-called pi theorem of dimensional 
analysis has even been taken to mean that the 


construction of a representative model is al- 
ways possible, although it is generally held that 
the strictly mathematical form of the theorem 
is to be preferred in any venture short of philo- 
sophical reflection. 

We shall deal with models of the dynamic 
variety only, which thus involve time as a prin- 
cipal variable. Furthermore the transient state 
is of greater interest here than either the steady 
state or the static state, as in statics, although 
these conditions of equilibrium are attainable 
in, and may be studied by, the more general 
transient-bearing systems under consideration. 
Quite commonly time in an original physical 
system is reflected as time in the model, albeit 
with a scale factor which may range from a 
small fraction to a large number. The inter- 
change of some other dimension for time, or of 
time for some other dimension, may also be 
arranged for, and time may be eliminated al- 
together in a model, or again employed in cases 
where it did not occur as an important factor 
at all in the original. Time, as do all variables, 
appears as an angle in a mechanical differential 
analyzer. In the electric and electronic models 
to be discussed, time is generally preserved 
intact, although stretched or shrunk beyond 
recognition. 

The most impressive models or synthetic 
representive structures are those in which one 
physical medium acts in place of another, op- 
erating thus by virtue of one or more of the 
many analogies which are demonstrable among 
components involving the known physical 
media. Of such analogies the better understood 
are those among mechanical, electrical, and 
thermal processes, where we include under 
mechanical processes such variants as hy- 
draulic and pneumatic ones. All such processes 
are self-analogous under the duality transfor- 
mation, with the interchange of potential and 
kinetic energy. With regard to energy the ther- 
mal case is exceptional in that the usual anal- 
ogy which is established makes electromotive 
force, for example, correspond to temperature. 


48 





eOi^FIDENTIAL 


THE PHILOSOPHY OF MODELS 


49 


both quantities acting as potentials. This anal- 
ogy leads logically to the identification of 
quantity-of-heat with quantity-of-charge, of 
which only one is truly energy. The preserva- 
tion of energy, however, in such postulation of 
analogous correspondences in model techniques, 
is by no means essential. It even forms a re- 
striction in scope. When several media combine, 
however, in a model or in any useful system to 
be studied, then it is of the greatest convenience 
to employ analogies which preserve energy. 

A distinction must be clearly emphasized 
between the various model structures, synthetic 
and simulative devices, and physical repre- 
sentations (which we shall henceforth refer to, 
for the most part, simply as simulators) which 
are constructed and employed in the laboratory 
as tools of research and development, and 
those which are intended for applications 
wherein an operator deals with the simulative 
equipment as a substitute for another appara- 
tus represented thereby, and by such dealings 
familiarizes himself with the workings of the 
original apparatus under conditions which are 
relatively easier, cheaper, or safer. The em- 
ployment of synthetic trainers in fire control 
applications is a good example of the latter 
category of usefulness, and is possible when- 
ever the effectiveness of a given man-machine 
interaction is important in the operation of an 
aiming-control system. Generally even an 
approximate simulation of the dynamical rela- 
tions, with which the operator must associate 
himself in such circumstances, is sufficient for 
his indoctrination or for the perpetuation of his 
skill through practice. It is a common experi- 
ence, however, for a simulator which has been 
developed for the first-mentioned purpose, for 
purely laboratory purposes, that is, in the ex- 
ploration of new or proposed physical arrange- 
ments, to find incidental or ultimate application 
as a training device. In some such cases there 
has been confusion over which end was being 
served by a particular equipment; and not in- 
frequently a trainer, in which certain approxi- 
mations had been allowed as inconsequential to 
the needs of that function, has been miscon- 
strued as presuming to embody the detailed 
characteristics of a complex fire-control system 
together with the relevant relationships among 


combatants, projectile, and the geometry of 
space. The possibility of such misinterpreta- 
tion, which might appear trivial from a larger 
viewpoint, has been of very real importance in 
several developmental endeavors. It is worth 
guarding against even in the makeshift opera- 
tions which are typical of an emergency. A 
sharp line should be drawn, whenever more 
than a single homogeneous group becomes in- 
volved, between the laboratory simulator and 
the trainer into which as a separate issue it 
may be transformed. 

An intermediate category must now be men- 
tioned, at the risk of diffusing the dividing 
boundary already indicated. Simulators may 
be constructed, in a form more permanent than 
is the case for the study phase in research, for 
the express purpose of teaching what is already 
known of the dynamics of a given physical sys- 
tem. These are not trainers, although they may 
certainly impart to the user a facility in carry- 
ing out such operations as the adjustment of 
parameters in an automatic apparatus to give 
maximum performance and stability. A simu- 
lator of this type might be called an educational 
simulator. In typical circumstance it may also 
stem out of the availability of a developmental 
simulator, as in the case of the training simu- 
lators already discussed. In this report an effort 
shall be expended to distinguish faithfully 
among all these separate types. 

Finally, we cannot conclude this general dis- 
cussion of models, of which our simulators are 
only a special case, without citing the purest 
model of all, namely the medium of the mathe- 
matician. The symbolism of variables, func- 
tions, operations, and equations, taken in 
company with the rules which they follow, 
form what is almost the ultimate in flexible 
models. Thus the symbol for a variable is truly 
the analog of its physical embodiment, an equa- 
tion of some physical truth which is stated or 
proposed. The manipulation of the physical 
model is directly reflected in the manipulation 
of the mathematical model, or of the symbols 
belonging thereto. Thus it is not surprising 
that an underlying standard for the sufficiency 
of a model is aptly provided by comparing the 
equations of model and prototype. To go a step 
further, consider the wave function of the math- 


.CONFIDENTIAL,-) 


50 


SIMULATION AS AN AID IN DEVELOPMENT 


ematical physicist. There he has a model 
without tangible physical counterpart, but 
which describes in some detail a complex rela- 
tionship having properties which agree with 
ascertainable data on the ‘‘unknown’" physical 
entity. Why ask for more ? Prediction is all that 
counts, ideally. But this is already too far afield. 
We should soon be discussing words and lan- 
gauge as models (which of course they are). 

^2 BACKGROUND FOR ELECTRONIC 
REPRESENTATION 

Before turning to the use of vacuum tubes 
in simulative applications, we shall dispose here 
of several items which will not be dealt with 
exhaustively but which will serve to define the 
general field of investigation. These items shall 
also not appear, in any detail, elsewhere in the 
present report. 

First, as an example of a model structure of 
the mechanical variety, there is the so-called 
pursuit-collision course plotter."^ This plotter, 
which is a model of the purest geometrical sort, 
was needed to study the approach paths which 
might be obtained with the type of toss bomb- 
ing equipment known as the DBS. A gyro 
method was involved wherein a mirror in the 
optical sight was positioned through linear 
combination of a stabilized direction and the 
frame of the airplane. Relatively tight coupling 
to the airplane was being considered. It was of 
interest to determine the constants of such 
coupling so that the maximum allowance would 
be realized for target motion in the air mass. 
The problems being reduced to a single plane, 
the positions of the target and of the attack- 
ing plane were simulated by moving points 
on a board. Each point belonged to a system 
which had traction with the board through 
toothed wheels so geared as to establish the 
proper ratio of velocities. The markings of the 
teeth on paper provided a calibrated record; 
the direction of motion being provided by the 
orientation of the tractive wheels, and a tan- 
gent to the airplane path being periodically 

a Proposed by M. Alkan and constructed by Section 
7.2 through a contract with Stanolind Corporation in 
Tulsa, Oklahoma. See Prefatory Comments. This de- 
vice was supplied to the Bureau of Ordnance, Navy 
Department. 


determined by recording the position of an ex- 
tending member along the orientation of the 
corresponding wheel. The latter orientation it- 
self was continuously determined by linkage 
so as to turn, with respect to the established 
coordinate system, in adjustable ratio to the 
turning of the connecting line to the target. 
This “simulator” found practical use in the 
application intended, and aided in the deter- 
mination of parameters which, according to 
graphical tests on the records produced, yielded 
an optimum correction for the errors against 
which the general method was proposed. 

A similar device was developed at Mount 
Wilson, for the study of plane-to-plane attacks, 
which undertook to represent pursuit and fir- 
ing courses, and which latterly was modified 
to include an embodiment of aerodynamic skid. 
(A description of this work is available in 
OSRD Report No. 4737, issued under the spon- 
sorship of NDRC Section 16.1.) The resulting 
apparatus is a second example of a purely me- 
chanical simulator which has had application 
in airborne fire-control development and re- 
search. 

In the immediately preceding chapter we 
mentioned the experimental study of tracking 
which was conducted chiefiy at The Franklin 
Institute by Section 7.2. This research, which 
was entirely for fiexible gunnery and dealt 
principally with “classical” tracking aids and 
disturbed sights, will not be described here in 
any detail even though simulative techniques 
were used in both mechanical and electronic 
phases. One reason for this reticence is that 
most of this work did not come under the im- 
mediate supervision of the writer ; another and 
more plausible reason is that it will presumably 
be reported upon, as fiexible gunnery lore, by 
others connected with Section 7.2. 

The simulative electronics to be discussed as 
part of our research involvement in aiming 
controls includes studies on the control of 
guided bombs AZON, RAZON, and ROC 
(Chapter 8), and that branch of the PUSS 
project in which simulation of the dynamic re- 
sponses to airplane controls was carried out. 
This latter effort was only beginning to attain 
a practical stage at thg end of hostilities. We 
shall treat these separate topics in sections 


''^ONTlbENTIALl 


BACKGROUND FOR ELECTRONIC REPRESENTATION 


51 


below. First a brief discussion will be given of 
an earlier application of electronic simulation, 
made by the writer in connection with studies 
on automatic regulation at The Foxboro Co. 

Beginning in 1938, the writer was authorized 
to construct a series of electronic models, pro- 
posed in detail by him, for use in research on 
desirable dynamic characteristics for the con- 
trollers and/or regulators of industry. Al- 
though it was not uncommon then to use 
equivalent networks for synthetic studies on 
the dynamic characteristics of such apparatus 
as thermal and mechanical, a number of new 
techniques had to be invented for the regula- 
tory study. An arrangement was devised, using 
individually ‘Ted-back” components, for syn- 
thesizing the whole closed loop under automatic 
operation. One component represented the sys- 
tem being regulated, and adjustments were 
provided for convenient alteration of the con- 
stants to allow the synthesis of a great variety 
of such systems. Another component repre- 
sented the regulator or automatic controller 
under consideration, and adjustments afforded 
similar flexibility there, so that not only exist- 
ing types but newer proposals could be con- 
jured up rapidly. Provision was made for ap- 
propriately foiming the dual connection be- 
tween these components, and for incorporation 
of the disturbances against which the regulator 
must act. Such disturbances included sudden 
alterations in the desired value in addition to 
other equilibrium upsetting factors throughout 
the system; any type or degree of disturbance 
could be chosen at will. Repetition of the dis- 
turbance periodically, and display of a crucial 
variable of the loop on an oscilloscope against 
a time sweep in synchronism with the dis- 
turbance, afforded an apparently instantaneous 
picture of the recovery transient followed un- 
der regulation. Parametric adjustments had 
immediate effect on this graph, and could be 
continued until the desired stability and per- 
formance was in evidence. 

Since this original work was undertaken, 
similar developments have been reported else- 
where. We quote, for example, from a (con- 
fidential) British publication.'^ 

The study and design of cyclic dynamical systems, 
such as servo mechanisms, is complicated by a variety 
of factors amongst the most important of which are the 


high orders of the differential equations of motion and 
. . . non-linearities . . . However, even when these non- 
linearities are small it is still a matter of considerable 
difficulty to decide upon the most desirable ratios be- 
tween the various parameters of the system, and the 
choice between different types of internal feedback 
systems may have to be made on rather dubious 
premises, due to the severe analytical difficulties. 

The use of the electrically equivalent network of 
the system to be investigated provides the basis of a 
method which has proved to be most powerful in the 
resolution of these difficulties. 

Briefly, the method is to construct the equivalent 
electrical network, modifying it as may be convenient 
according to chosen scales of impedance and time, and 
to feed it with signals which simulate one feature or 
another of the normal “master system,’^ denoting by 
this phrase the mechanism which the servo system is to 
follow. A feedback path is provided, so that the signals 
taken from it may correspond to some characteristic 
feature of the “slave” or servo mechanism. The two 
sets of signals, “master” and “slave,” are then added 
by appropriate means. In order to facilitate the study 
of the results obtained, the input signals are applied 
and removed regularly, so that the system as a whole 
is taken repeatedly through a work-rest cycle, the rest 
period being chosen of sufficient duration to permit of 
the subsidence of any transients that may be set up. 
If the time scale used in the construction of the net- 
work is suitable, the period of the whole cycle of opera- 
tions may be made small enough to allow of the repre- 
sentation of the results on the screen of a cathode ray 
oscillograph tube, in the form of an apparently sta- 
tionary picture. 

The above quotation might equally well have 
been taken from descriptions of the writer's 
proposals made in 1938, except for certain 
differences in nomenclature. From that time 
until 1941 he had constructed several such 
simulators and had applied them in the de- 
velopment of improved controllers and in the 
successful automatic operation of certain in- 
dustrial systems. One of the most unexpected 
results was the use of the simulative equipment 
in the education of technicians who had to 
meet the problems of analysis, specification, 
and adjustment in the field. A session with the 
simulator substituted for a long interval of 
arduous experience with the practical problems 
of the mill and plant. 

Of such a synthesizer or simulator, there are 
several significant methods of operation other 
than that described above, although that was 
most familiar to the practical worker, who saw 
the transients of the recorder charts right there 
on the scope. Frequency analyses could be run 


52 


SIMULATION AS AN AID IN DEVELOPMENT 


directly on the machine. Related variables 
could be plotted directly against one another, 
eliminating the time variable. Random disturb- 
ances, rather than simple periodic ones, could 
be imposed; this was revealing owing to their 
broad energy content over a wide band of 
frequencies. For this purpose ordinary tube 
noise was used. The writer naturally sought to 
apply similar techniques when, beginning in 
1942 , he met analogous problems in the design 
of aiming controls. That this applicability was 
not illusory is attested to by the several war 
projects in which useful ends have been served 
in dynamical studies by electronic simulation. 
Certain of the tricks employed earlier for regu- 
latory studies have not been applied in the 
latter work, and the writer is rather eager to 
return to those studies, for servomechanism re- 
search and other applications, using the im- 
proved electric and electronic components more 
recently available. Somewhat more generally, 
it is felt that electronic simulative techniques 
will find growing and widespread usefulness 
for many recondite questions, both practical 
and academic, owing to the broad powers of 
representation embodied therein and to the 
speed with which exploratory manipulation 
may be performed in the laboratory. 

FEEDBACK AMPLIFIERS 12,3,4,6 

The application of such amplifiers to simu- 
lative developments forms one of the most es- 
sential techniques in that art. Applied thus, the 
stability of the feedback circuit becomes of 
primary interest, leading to the remarkable 
situation in which stability studies as such are 
enhanced by the use of systems involving a set 
of feedback amplifiers, in the individual design 
of which such stability studies may be invalua- 
ble. But such a circumstance is not uncommon 
in research, where the talents of the detective, 
and dispassionate reasoning in general, find 
limitless opportunities. 

It will be assumed here that the reader is 
familiar with the standard passive networks 
and with the corresponding dynamical systems 
which may be represented thereby without the 
necessity for feedback methods. Of the stand- 
ard circuit elements only the resistor and the 


capacitor need be used in electronic simula- 
tion, and it is fortunate that these elements are 
available commercially in relatively pure, or 
“ideal,” form. 

There are two principal kinds of feedback in 
electronic circuits, which with their variations 
and mixtures have fundamental importance in 
simulative circuits. Cathode feedback and plate 
feedback, so called, comprise these two basic 
types, the names referring to the branches of 
the tube circuits in which retroactive opera- 
tions are made to occur. Alternative terminol- 
ogy identifies these as current feedback and 
voltage feedback, respectively, in recognition 
of the electrical mode which acts most pre- 
dominately in the two cases. In Figure 1 is 



Figure 1. Cathode feedback circuit. 

shown the fundamental cathode feedback cir- 
cuit, or cathode follower adaptation, which was 
earlier employed by the writer in simulative 
assemblies. The inclusion of such material here 
does not imply that it carries classification. 
Much of the earlier work has been public 
knowledge, albeit not widespread. The writer 
had prepared and may publish descriptions of 
such work as applied to unclassified categories 
of engineering. A brief explanation should suf- 
fice. Since opposing currents circuits are pro- 
duced in the impedance Zi by the sources Ei 
and E2y the voltage ei tends to follow the input 
voltage eo owing to the effect of the difference 
of these two voltages on the plate resistance 


FEEDBACK AMPLIFIERS 


53 


of the tube. For proper choice of tube (prefera- 
bly of high transconductance) and circuit con- 
stants, the error between eo and Ci may be kept 
very small, provided of course that stable op- 
eration is attained. Thus eo may be “followed” 
very closely by ei. Whereas eo may occur in a 
low-power-level circuit, and may be surrounded 
by high impedances, the very high grid re- 
sistance at which the present tube can be oper- 
ated insures the relative noninterference with 
Co in its natural environment. Furthermore, 
power may be drawn from the circuit at Ci 
since the feedback works to maintain this 
voltage in spite of applied loads, within con- 
siderable limits. Thus we have an important 
tool already, namely, an isolating or buffer 
amplifier, with unit gain. If now no current is 
drawn externally either from Co or C2, and the 
sources Ei and E2 are exclusively involved in 
the present circuit, then the current in the 
impedances Zi and Z2 must be equal. Thus 
^2/^1 + ^2/^1 — 0 , or approximately eje^ 
= —ZJZ^. Now if C2 is repeated by a sub- 
sequent buffer amplifier, a means is provided 
by the representation of many operational 
characteristics. If in particular the two im- 
pedances are simply equal resistors, a polar- 
ity reverser or phase inverter, so called, 
results. For integration with respect to time, 
Z2 may be a capacitor and Zi a resistor. Con- 
versely, for differentiation with respect to time, 
the roles of resistor and capacitor may be re- 
versed. The generalizations which are possible 
may easily be imagined. Initial conditions are 
imposed in straightforward ways, although 
certain ingenious processes have become use- 
ful. In the above integrator, the lower limit of 
integration may be established at any time 
simply by imposing a momentary short across 
the capacitor. A typical simulator may com- 
prise a number of such feedback components, 
interconnected either directly or through the 
appropriate passive networks. In this proce- 
dure, criteria such as that of impedance-match- 
ing may be forgotten. Addition, or the forma- 
tion of linear combinations, for two or more 
voltages, and hence of the variables which 
these voltages represent, may be carried out 
in a number of ways with the basic circuit of 
Figure 1 . For example, several such feedback 


circuits may be arranged to possess the im- 
pedance Z2 in common. Or again, these volt- 
ages may be connected by a high-resistance 
dissipative network in such a way that eo is 
proportional to the desired sum or linear com- 
bination, although care must then be taken 
not to load the previous systems. For subtrac- 
tion one may always phase invert an odd num- 
ber of times. The only failing of the cathode 
feedback circuit, as shown, is the necessity for 
at least one “high” battery (Ei). The anode 
source (£'2), of course, must also be “high” un- 
less Z2 is zero, as it may be in the simple isolat- 
ing amplifier, for example. Thus each such cir- 
cuit must have at least one voltage source to 
itself. This requirement, however, has not been 
found too great a burden in the laboratory, 
since the drain may be kept quite small. The 
writer used a large bank of dry batteries for 
this purpose, in his own work, carefully 
shielded to prevent capacitive interstage 
coupling, and found it adequate to replace 
them every two years. Modifications are possi- 
ble which will permit the adaptation of such 
circuits to single-source powering, but such 
sources must be meticulously regulated to 
present zero impedance and hence zero coupling 
between the using channels. Furthermore, such 
modifications complicate the circuits so much 
that plate feedback might as well be used. We 
now turn to plate feedback. 

A common plate voltage source suffices for 
the plate feedback circuit, shown in Figure 2 , 



Figure 2, Plate feedback circuit. 


if the high-gain d-c amplifier which is involved 
(see Figure 3 ) is properly designed. In this 
connection the term “high-gain” is employed 
in a relative sense only, as compared, for ex- 
ample, to the unity-gain isolating amplifier. 
(The gain figures for typical a-c amplifiers are 
not referred to in this context.) Only one such 




.CONFIDENTIAL 


54 


SIMULATION AS AN AID IN DEVELOPMENT 


design is here shown. As suggested above, the 
supply sources should be well regulated. Re- 
ferring to Figure 2, it should be remarked that 
the function of the amplifier shown there in the 

(eg) 



block is to convert the small balance voltage 
Ae into a corresponding but much expanded 
variation in the voltage Cg, and to reverse the 
sign. The effect is to keep the voltage Ac very 
near zero. As above in the current-feedback 
circuit, the point of operation (for the first 
tube) is so chosen that the grid input im- 
pedance is very high. Thus the currents in the 
impedances Zi and are substantially equal. 
Hence as before, eje^ = — ZjZ ^ ; and may 
be loaded within reasonable bounds. The op- 
eration of addition on several variables may 
be carried out, as in the second method men- 
tioned above for the cathode feedback circuit, 
by substituting a number of resistive paths 
for Zi, Z 2 being also resistive, and each such 


path initiating at one of the variable voltages 
to be summed or combined. The coefficients of 
combination are adjustable by the separate 
connecting resistances. 

There are a certain number of feedback ap- 
plications which do not fall into those types 
above classified. For example it is possible 
thus to provide circuits which have extremely 
long time constants, or long ‘‘lags’’ of low or- 
der, for special purposes. Such time constants 
are well in excess of those obtainable passively, 
even with the largest resistance and capaci- 
tance values available in the laboratory. Rep- 
resentation of the various kinds of servomech- 
anisms or degenerative “telemeters” in proto- 
type systems, as is to be expected, may be ac- 
complished^ quite straightforwardly by elec- 
tronic feedback components in the process of 
simulative construction. 

OTHER SIMULATIVE COMPONENTS 
AND COMBINATIONS 

The amplifier circuits already referred to 
enable the experimenter to prepare, for his 
edification, extremely flexible models of dy- 
namical systems. By simple interconnection, 
he may readily assemble the counterpart of 
any physical entity governed by a linear dif- 
ferential equation, of finite order, with con- 
stant coefficients. But he is not thus limited, 
although within this realm lie many significant 
dynamic relationships of sorts now submitted 
to analysis. For the larger class of linear rela- 
tions represented by equations with coefficients 
which vary with the independent variable, here 
time, a programming of the adjustable parame- 
ters suffices. Similarly nonhomogeneous rela- 
tions, with prescribed “forcing functions” (un- 
fortunate phrase!), are representable. The 
greatest advantage of this kind of simulation, 
however, and the crux of its power, in relation 
to competitive methods, is the ability in simple 
manner to incorporate nonlinear dynamics. We 
need not speak of the analytic difficulties which 
are there involved, nor of the physical impor- 
tance of nonlinear systems in general. Suffice 
it to say that the resulting problems preoccupy 
and harass some of the best available mathe- 
matical brains. 




OTHER SIMULATIVE COMPONENTS AND COMBINATIONS 


55 


One very simple source of nonlinearity is the 
presence of a mere boundary in the range of 
a variable. Many examples may be cited, and 
may amply be supplied by the reader. Probably 
the simplest examples are furnished by trans- 
formations from a given variable to a function 
thereof which is either nonincreasing or non- 
decreasing over the entire range to be con- 
sidered, and in which for at least certain por- 
tions of the range the function is unchanging. 
An instance is shown in Figure 4. The elec- 



R 



specifications: 

1. R LARGE COMPARED WITH "CLOSED" RESISTANCE 

OF DIODES 

2. R AND R COMPARABLE WITH "OPEN" RESISTANCE 

OF DIODES 

Figure 4, Boundary function and its simulative 
counterpart. 

tronic embodiment of such a transformation 
is simple. It may involve only a pair of rectify- 
ing diodes, as contained for example in a 6H6 
tube, so biased that voltages corresponding to 
variation of the first variable beyond the 
bounded interval produce no further change in 
the function of, or the transformed version of, 
that variable. Such an arrangement, shown 
also in Figure 4, must always be approximate, 
but the approximation may be refined to any 
desired degree by appropriate choice of the 
electrical circumstances. Only one type of non- 
linear component is thus illustrated; it is evi- 
dent, however, that by combination of such 


circuits a great variety of similar, and more 
intricate, relations may be embodied. Nor are 
we restricted to functional relations repre- 
sentable graphically by a single curve, or 
analytically by single-valued dependences. Such 
physical relationships as inertness, when for 
example there is backlash or play in a mechani- 
cal connection, may be simulated through the 
application of biased rectifiers in circuits where 
charge may be stored over reasonable inter- 
vals. In general, the inclusion of major non- 
linearities of this sort alter fundamentally the 
stability considerations in control systems or 
in any apparatus where the dynamic perform- 
ance is of interest. It is thus of great impor- 
tance to be able to treat such nonlinearities 
without the endless drudgery which is essen- 
tial when straightforward analysis is the only 
recourse, however otherwise educational or 
character-building such a process may be for 
the performer. 

A useful tool in simulation, for that general 
class of dynamics, particularly, in which non- 
linear relations are included (it might have 
been more appropriate earlier to have defined 
nonlinear systems as those in which the addi- 
tivity or superposition principle does not ap- 
ply), is the follower or servomechanism which 
transforms voltage into a corresponding ’ re- 
sistance. Consider first the case in which pro- 
portional correspondence is enforced. Many 
such components have been built and applied 
in the simulative ventures we have dealt in. 
The usefulness of such a properly made com- 
ponent, which is great, is not at all limited to 
the representation of nonlinearities, but ap- 
pears wherever the automatic manipulation of 
a resistor or potentiometer may be desired. The 
construction may be very neat and simple, and 
high speed and precision has been shown fairly 
easy to attain. Naturally the time constants of 
the response should be well below those which 
are involved, purposely, in the remainder of 
the simulative channel in which such a com- 
ponent occurs; it has been satisfactory to em- 
ploy pairs of circular, wire-wound potentiom- 
eters driven by small d-c motors energized 
either from polarized relays or from vacuum 
tube circuits. The error signal, which is sup- 
plied to an interpreting network and thence 


fcONFIDENTIAL 


56 


SIMULATION AS AN AID IN DEVELOPMENT 


to the motor circuit, is derived both from the 
input voltage and from the voltage division of 
one of the driven potentiometers. The other po- 
tentiometer, driven for example in tandem with 
the first, provides a free resistor having re- 
sistance proportional, say, to the input voltage. 
Before turning to some applications of the pro- 
portional form, we merely mention that the 
introduction of any appropriate function may 
be accomplished, through the voltage-to-re- 
sistance follower, by embodiment of such func- 
tion in the resistance versus motion law of the 
final resistor, or of its reciprocal or inverse in 
that of the follower-resistor itself. 

A means for rapid conversion of a voltage 
into a proportional resistance enables the reali- 
zation of many fiights of fancy. We record only 
the soberer of these possibilities. It will be 
evident that certain of these may also be ef- 
fected by logically simpler means, but we note 
that there is large advantage, for such pur- 
poses, in the repeated application of a given 
type of basic component. 

Having a feedback amplifier, of either type 
above described, with the associated pair of 
impedances restricted to a pair of resistances, 
then it is possible, by making either such re- 
sistance proportional to a separate external 
voltage, to perform multiplication or division 
among voltages in various ways. The result- 
ing product or quotient has also the form of 
a voltage. While those variables which are re- 
fiected in the resistance of either resistor pair 
cannot normally be made to take on negative 
values, or in certain cases even zero, modifica- 
tions are possible whereby equivalent varia- 
tion can be permitted. A general case is given 
by that in which the input voltage of the feed- 
back amplifier is employed together with those 
which, respectively, set proportionally the “in- 
puf and ^‘output’' resistances thereof. Here 
the output voltage is proportional, through any 
desired factor of scale, to the ratio of the prod- 
uct of the first two voltages to the third voltage. 
Simple products or ratios, as well as recipro- 
cals, may then be evaluated in a single com- 
ponent. Through duplicate roles, for example, 
a voltage, or rather the variable thereby rep- 
sented, may be squared through multiplica- 
tion into itself. By including such an arrange- 


ment within a more comprehensive feedback 
loop, inverse operations such as the extraction 
of the square root may be performed. Out of 
necessity, we are speaking here only of real 
variables. With combinations of similar com- 
ponents, in series or cascade, it is evident that 
such delicate operations may be carried out as 
the raising of a variable to any fixed rational 
power. This type of conversion, of course, may 
be accompanied by any (otherwise) linear dy- 
namic operation of the classes already men- 
tioned. 

Consider now integration with respect to 
variables other than time, or in general with 
respect to an arbitrary independent variable. 
An arrangement was proposed^ for this pur- 
pose, but was not constructed practically for 
a variety of reasons, principally because no 
need persisted for it which was not more easily 
satisfied by other means. Consider a time in- 
tegrator as described, with fixed resistive and 
capacitive elements, and let it be supplied 
as input with a voltage which is the product, 
obtained as already indicated, of a primary 
voltage (preferably, in this case, always of 
one sign) and the time derivative, evaluated 
in the regular feedback manner, of a second 
input voltage 62- The output voltage of the 
time integrator is thus the integral of the volt- 
age ei with respect to the voltage 62. Thus 


1 de2 

/ -ei — 

RCjto dt 




ei de2 . 


Within certain limitations, of which it is not 
difficult to imagine the removal, and with pre- 
cision of the order of 0.001 to 0.01, it is evi- 
dent that this more general type of integration 
is feasible, and the potentialities of electronic 
simulation are thus extended to the dynamical 
realms of the better-known differential ana- 
lyzer. Much practical development, however, 
remains to be completed along these lines, al- 
though only the fundamental elements already 
treated need be involved. 

Returning momentarily to linear systems, 
with the continued implication none the less 
of nonlinear generalizations and ramifications, 

*’We should like to acknowledge the collaboration of 
Loebe Julie in connection with this item, and also with 
certain other conjectural plans for electronic simulative 
measures which are referred to here. 


OTHER SIMULATIVE COMPONENTS AND COMBINATIONS 


57 


we mention two types of assembly which are 
of interest in simulative structures and which 
are singularly adapted to electronic techniques. 
One is the approximation of pure time lag, or 
of a direct shift of a function along the axis 
of time (or of another independent variable, 
by extension of the method), which may be 
achieved through recognition of the limit 



Several methods are available, each using a 
chain or cascade of feedback circuits to pre- 
vent the passage of energy except in one di- 
rection along the chain. A possible circuit for 
M = 4 is shown in Figure 5, where cathode fol- 



Figure 5. Cascade of cathode followers as lag. 

lowers (reference Figure 1) are employed. 
Naturally any number of such sections may be 
used, and the larger the corresponding value 
of 7^, the closer the approach to a pure time 
lag. A useful approximate network for cases 
when small n suffices is shown in Figure 6, 



Figure 6. Passive approximation to Figure 5. 


the number of sections being limited by the 
available magnitudes of resistance and capaci- 
tance. Note that each section has the same (un- 
terminated) time constant, and that the energy 
transmission grows progressively smaller from 
input to output. 

Another useful assemblage of the elements 
noted above may be used to synthesize any 


linear relationship which may be adequately 
described by a rational function of the deriva- 
tive operator, we assume for simplicity with 
respect to time. Such an operator is 

m 

2 diP' 

R(P) 

i=o 

where it is understood that = ho = 1. For 
purposes of exposition assume that neither m 
nor n is greater than 5. Fractional differentia- 
tion and fractional integration are not con- 
sidered here. Distributed systems are essential 
to the precise representation of such opera- 
tions, but again approximations by lumped 
systems of low order not infrequently suffice. 
We make use, for the simulation of R(p)f of 
the well-known operational characteristic of a 
feedback system. The denominator is obtained 
by feeding back a linear combination of the 
branch outputs of a chain of differentiators, 
the input to the first differentiator being made 
the difference between an input voltage and the 
given linear combination. We obtain thus, 
familiarly, 

i + ic,X 

j=0 / 

as the operator describing the relation borne 
by the input difference to the input voltage. 
The separate unity term may be eliminated by 
setting Co = 0, thus reproducing (with the 
equivalence hj = c^; j = 1, 2, . . . 5) the 
earlier denominator. The numerator, and the 
desired total characteristic is now created 
merely by taking a new linear combination 
from the same chain of amplifiers. Figure 7 
shows the assembled system, in which plate 
feedback systems, of the type shown in Figure 
2, are employed. The coefficients of R(p) are 
of course directly adjustable negative values 
requiring the addition of a ‘'phase inverter’' 
in each such case. This arrangement, with ap- 
propriate means for insertions of forcing func- 
tions and for presentation, is extremely educa- 
tional in the laboratory. A number of interest- 
ing modifications are possible. By division of 
both numerator and denominator by p^ or p^. 



58 


SIMULATION AS AN AID IN DEVELOPMENT 


whichever is the higher power, and whenever 
such an operation is rigorously permitted, we 
may obtain a rational function of the defi- 
nite time integrator, and proceed exactly as 
above except with the replacement of each dif- 


■ ► DC AMPLIFIER 



embodied: 

(bo=l) 

Figure 7. Simulative connections for class of linear 
operation. 

ferentiator by an integrator. For many pur- 
poses this is preferable ; for example it is easier 
then to establish initial conditions. 

When certain variables in a physical system 
to be simulated are related by complex static 
functions, meaning by this term that time is 
not fundamentally involved, it may be conve- 
nient to represent such functional relations by 
a mechanical linkage rather than through a 
combination of electronic elements as such. 
Such linkages may involve any number of 
inputs, and may sometimes have more than one 
output. They are similar to computing linkages 
for full-scale aiming controls, as described in 
a separate chapter of this report. Angular mo- 
tion is practically most convenient for the input 
and output variables, such motion being most 
readily provided, in electronic (in this case 
electronic plus mechanical) simulators, by the 
resistive follower which correlates mechanical 


angle with resistance, hence with voltage. An- 
gular outputs of the linkage may conversely be 
accepted as resistance, since reasonable power 
is available from the feedback inputs, and 
thereby converted again into voltage. The re- 
sult in effect is an extremely flexible form of 
‘"static” computer, entirely surrounded by volt- 
ages. By proper design of the linkages, in 
which the same engineering principles apply 
as with the more worldly types discussed else- 
where, high speed and reliability may be ob- 
tained. There have as yet, in our work, been 
few occasions for elaborate linkage compo- 
nents in this role, but the potentialities, say for 
intricate aerodynamic interrelations, are prac- 
tically unlimited. A large attraction is the ease 
with which modifications in the nature of the 
functions may be incorporated, for example 
through alteration of link lengths and pivot 
positions. 

It may be repeated that the general technique 
of electronic simulation has great flexibility 
with regard to the scale factors of analog ver- 
sus prototype. The possible extremes of speed 
and sluggishness are relatively far apart. This 
applies, of course, only to the time scale ; other 
dimensions are correspondingly adaptable. 
Further as to time, one of the principal fields 
of application for this type of simulation has 
been to systems involving a human element, 
and here the time scale must be religiously rep- 
resented as it exists in the full-scale apparatus 
being represented. The man as a machine has 
nonadjustable time parameters, or rather he is 
the component which cannot be altered, except 
by a certain amount of learning, as a result 
of the research, and must therefore be ac- 
cepted as is, whether trained or untrained. 
Since the remainder of the model must be 
adapted to him, particularly with regard to 
time scale, it is welcome that electronic struc- 
tures find little difficulty in being thus adapted. 
Of course in any such case, with a human “com- 
ponent,” many other provisions must be made 
to achieve naturalism. 

4 5 SIMULATION OF FLARE-BOMB GUIDING 

The projects connected with the development 
of aiming-control systems for the phorodromic 
and pseudophorodromic guiding of the bombs 



IpJONFIDl^TiAf:) 



SIMULATION OF FLARE-BOMB GUIDING 


59 


AZON, RAZON, and ROC are discussed more 
generally in other parts of this report. Elec- 
tronic simulation, however, played a crucial 
role in these projects, as in others, and it is 
considered appropriate to treat here the sev- 
eral such simulators which were constructed 
and employed by us in this work. 

As a guided bomb of this general type (we 
refer to what are called high-angle bombs) fell 
toward the target, the guiding operator was 
instructed so to operate the controls at his end 
of the radio link, from above in the bomber, 
that either the flare of the bomb itself or an 
image thereof synthetically produced was held 
superimposed on the selected target beneath. 
This operation was one- or two-dimensional, in 
dependence on the class of missile and on the 
preferred mode of operation. Accuracy of the 
bomb fall depended heavily on the accuracy 
with which the above superposition was car- 
ried out, at the moment particularly when the 
missile arrived at the level of the target. Thus 
the stability and the other dynamic character- 
istics of the guiding process were of prime in- 
terest. Having a considerable familiarity with 
the space paths and guiding responses of such 
bombs (Chapter 8) through three-dimensional 
solutions which we had obtained from the new 
differential analyzer at MIT, and having seen 
the excellent correlation which was evident be- 
tween these solutions and full-scale tests, we 
were in a good position to determine and to 
recommend the dynamical nature of electronic 
simulators which would represent the process 
sufficiently well to an operator in the labora- 
tory. In the course of development a number 
of such simulative equipments were prepared, 
of various degrees of precision and excellence, 
and these were usefully applied to the research 
problems which arose and to the training needs 
which appeared in connection with full-scale 
tests. We shall include below a description of 
those features of these equipments which are 
of interest from the simulative standpoint. 

In the case of each of the bombs referred to, 
the operator sends messages to it via the radio 
link by means directly of the angular motion 
of a handle in front of him. His means of 
manipulation, sometimes in one angular dimen- 
sion and sometimes in two, is thus analogous 


both to the handlebars of a turret control, in 
flexible gunnery, and to the pilot’s control stick 
or column, in fixed gunnery or in other pilot’s 
fire control procedures. The handle in some 
cases operates merely a double-throw switch, 
and in others operates potentiometers, either 
one or two of each depending on the dimen- 
sionality of the control. Servo motors on the 
bomb are thus energized to move the control 
surfaces thereof. In the on-off case the sur- 
faces have three stable positions toward which 
they proceed for continual occupation, by the 
corresponding individual handle switch, of any 
of its three positions. In this case the velocity 
of motion in proceeding from one such posi- 
tion to another is constant, and reverses if a 
new position in the opposite sense is ordered 
during the motion. The velocity of such mo- 
tion is a property principally of the local bomb 
controls, and embodies an important design 
criterion, both for economy and for stability. 
On the latter question in particular, simulation 
proved to be an indispensable aid. To return 
to the manipulation, there is also a ‘‘corre- 
sponding” form of control, in which interme- 
diate positions of the control surfaces are held 
for continually occupied corresponding posi- 
tions of the control handle. This relationship 
is roughly proportional, handle position to con- 
trol surface position, and is also approached 
substantially at constant rate in the transient 
intervals. The simulation of these circum- 
stances is fairly direct. A standard control- 
handle is used as such, or duplicated, in the 
simulator, with either switches or potentiom- 
eters attached. Voltages thereby derived are 
followed by the voltages corresponding to the 
positions of the control surfaces through an 
electronic feedback precisely analogous to the 
bomb servos. The simulator circuit involves 
an amplifier as a sensitive relay, and an in- 
tegrator to imitate the constant rate of the 
servo-actuators in the bomb. The latter being 
roll-stabilized in practice, no “phasing” con- 
trols were necessary, and either one or two 
operators could be involved either for the real 
proceedings or for the simulator in the lab- 
oratory. 

We consider now the simulative presentation, 
by which the laboratory operator sees the re- 


b/CONFIDENTML 


60 


SIMULATION AS AN AID IN DEVELOPMENT 


suit of what he is doing. For our purposes, 
cathode-ray tubes (referred to hereinafter as 
oscilloscopes or scopes) were employed in all 
cases. The luminous point on the screen, cor- 
responding to the projected visual impression 
of the bomb flare, was observed to move in re- 
sponse both to the guiding operations and to 
disturbances, and to hover near, or in inexpert 
hands less near, a stationary spot correspond- 
ing to the target. In the case of AZON the 
target was typically a line, rather than a spot 
as for RAZON or ROC. Elaborations were in- 
troduced to promote realism. For example the 
surface of the scope screen was coplanar, in 
focus, with that of the image of an aerial pho- 
tograph, so that to the operator the flare ap- 
peared to move over the landscape, as in the 
real operation. Thus he could pick out targets 
at will or under direction from a superior in- 
telligence to which he was, or pretended to be, 
subordinate. Many games were thus possible 
for the promotion of guiding skill. Such fur- 
ther reflnements were possible as the gradual 
diminishment of the intensity of the spot on 
the scope as the bomb dropped, corresponding 
to the weaker brilliance of the flare as the 
bomb receded below, with a momentary bright- 
ening at the end for the detonation. The varia- 
tions are readily imaginable. 

Between the voltages corresponding to the 
positions of the control surfaces of the bomb 
and those deflecting the beam of the scope in 
correspondence to the direction of the bomb 
from the bomber is incorporated the simula- 
tive electronic channels which represent the 
physical dynamics which obtain between these 
variables. The lateral acceleration of the bomb, 
in one or two directions, is nearly propor- 
tional,'^ within significant limits, to the deflec- 
tions of the control surfaces, as well as to a 
function of the speed of the bomb and of its 
altitude. To a large degree it was shown ade- 
quate to neglect the angular dynamics of the 
bomb in response to the deflections, although 
representation of such phenomena is straight- 
forward. For purposes of the stability study, 

'The proportionality, in the case of RAZON for ex- 
ample, is different in each direction, or in “range’’ and 
in “azimuth,” so that a somewhat asymmetrical guiding 
response was employed in the simulators for a closer 
representation. 


and of the synthetic reproduction of guiding 
dynamics, it sufficed to consider the function of 
speed and altitude, affecting the spatial acceler- 
ation, as an appropriately chosen function of 
time, whereas in reality that function de- 
pended, although in a less serious manner, on 
the deflections themselves, via the drag func- 
tion and the geometry of the flight path of the 
missile. Thus the deflection voltages, after mul- 
tiplication, or division, by a selected function 
of the time since dropping, could be integrated 
twice with respect to time to produce voltages 
corresponding to the lateral motion of the 
bomb in the air mass. To obtain the direction 
of the bomb from the bomber, for simplicity 
assumed unaccelerated, it was only necessary 
to know the distance through which it had 
fallen, this being available quite closely, again 
as a function of the time. It should be evident 
how the components already described may be 
compounded to achieve this procedure. A pro- 
gramming device was allowed to introduce, as 
variable resistances, the time functions which 
entered. The independent effect of the distance 
to the bomb, or the perspective effect as it 
came to be called, was curiously impressive. 
If, in using the simulator, the bomb were left 
considerably off the mark in angle, and with 
no corrective guiding that is, its approach in 
angle toward the target as time wore on, owing 
to the simulation of decreasing parallax, was 
exactly as though it were a real bomb seen 
from a bomber, and was especially appreciated 
by those of us who had watched bombs go down 
in air trials. Further, it was a great comfort, for 
a different reason, to be able to guide them on to 
the target, but that is another matter. 

An essential feature of the bomb simulators 
is the embodiment, in the sense outlined above, 
of boundaries on the variation of the control 
surface deflection, which ran actually against 
stops, and on the rates of motion of these de- 
flections, which were limited by the capabili- 
ties of the bomb servo motors. The discon- 
tinuities thus involved were crucially important 
in the overall question of stability, and were 
incorporated in the simulators by means of 
biased rectifiers as already described. 

Numerous auxiliary controls are necessary, 
for the facile operation of such simulators, but 


t^?^i)ENTIAL 



SIMULATION OF TELEVISION BOMB GUIDING 


61 


these may be straightforwardly provided. One 
must be able to start the operation precipi- 
tately, having set in the desired initial condi- 
tions, of wind, initial dropping error, and so 
on. At the end of the time of flight, it is con- 
venient to freeze the bomb position for scor- 
ing, which may be accomplished by opening 
the capacitor circuits of the integrators, and 
then to return all adjustments quickly to the 
initial condition for the next “drop.” The form 
of such auxiliary controls depends greatly on 
whether the simulator is for laboratory study 
or for the rougher needs of a training device. 
Experience was gained with both such applica- 
tions, and fuller details may be found in the 
various contractors’ reports. (See Division 5, 
Volume 1.) 

SIMULATION OF TELEVISION 
BOMB GUIDING 

Although the ROC bomb was, at one point in 
its career, experimentally equipped with a flare 
for line-of-sight guiding, its initial purpose had 
been quite different. Primarily a vehicle for 
radar-homing, ROC was also adapted to embody 
the miniature television camera and transmitter 
(MIMO), the latter having been developed for 
suicide bombing by proxy. The missile, with 
MIMO, was to be dropped rather naturally 
toward a target as a bomb, and subsequently to 
be guided thereto by a remote operator, over a 
radio link in one direction, who saw the view ap- 
pearing to the forward-looking televising cam- 
era, which was transmitted over a radio link in 
the other direction. It is not intended here to 
describe this method or the ROC bomb, itself of 
great interest and significance, since partly this 
is a subject more nearly for the chapter on guided 
bombing and more particularly since much fuller 
reports are given by other agencies (Division 5 
of NDRC,for example) . The problems of guiding 
with which we were concerned, and for which we 
turned to simulative techniques of study, were 
problems of controls to give the optimum ap- 
proach, in terms of the probability of hitting, and 
of the stability of the processes in which such 
controls were to be involved. 

As before, a control handle is involved, both in 
the simulator and in the prototype system, but in 


this case it is exclusively two-dimensional and 
carries potentiometers for proportional manipu- 
lation of the bomb controls (although for certain 
studies a one-dimensional counterpart was con- 
sidered and employed) . The method of operation, 
otherwise, of the control surfaces over the radio 
link and through the bomb servos, is essentially 
as in the case of the normally phorodromic 
bombs. For these surfaces, the minimum run- 
out time, from zero to full deflection, is longer 
for ROC than for AZON and RAZON, and it was 
partly of interest to determine the effect of this 
parameter on the stability of guiding. As ex- 
pected, it turned out to be rather important from 
this standpoint. The scope presentation corre- 
sponds now to that on the screen of the television 
receiver. The target appears on both under the 
proper circumstances, in the one case as a single 
spot of fluorescence and in the other amid the 
landscape toward which the real bomb is head- 
ing. The lack of the illusion of changing perspec- 
tive, in the simulator, is partly repaired by the 
preservation there of the increasing angular 
response observed, in external objects such as 
the target, in answer to the maneuvering con- 
trols, as the bomb continues on its course. 

A second spot is presented on the simulator 
scope, differing geometrically from that repre- 
senting the target, as the analog of a movable 
reticle which has been proposed as an aid in guid- 
ing. This proposal, which has common elements 
for the various detailed methods which have been 
considered, involved the manipulation of the con- 
trol handle by the guiding operator in such a 
manner that the moving reticle was maintained 
on or near the image of the target. From the con- 
trol handle proceeded thus two paths of influence. 
One to the bomb controls via the radio link ; one 
to the moving reticle on the scope screen. The 
proposals for effective aids to guiding differed 
principally in the choice between these two in- 
fluence-paths for inclusion of aiding dynamics, 
and in the nature of the latter dynamics wher- 
ever placed. A service was done by the simulative 
equipment in the choice of these dynamic control 
adjuncts. 

Both the relative direction to the target, or 
lead angle, as represented by the departure of 
the target spot from the center of the scope, 
and the absolute direction of the target in 


'^confidentia; 


62 


SIMULATION AS AN AID IN DEVELOPMENT 


space, which is given also by the absolute 
direction of the bomb from the target, are 
simulated by varying voltages. The rate of turn 
of the bomb is taken as proportional to its 
lateral acceleration, and hence to the deflection 
of the control surfaces under guiding. It is also 
proportional to a function of speed and altitude, 
and hence adequately, in this case, to a function 
of the passage of time since release. Variation of 
the lead angle depends on the turn of the bomb, 
in the air mass, and on the rotation in space of 
the line of sight to the target. That is, there is a 
direct summation among these angles which may 
be simply incorporated in the simulator. In ad- 
dition, the rate of rotation of the line of sight is 
proportional, additively, to the product of the 
lead angle into the bomb speed and to the lateral 
speed of the target, and is inversely proportional 
to the range. The latter, again, is taken as a func- 
tion of the independent time variable. These rela- 
tions are adequate, when incorporated in simula- 
tive components of the type described, to present 
both the lead angle and the absolute direction as 
voltages in response to the operation of the bomb 
controls, via the handle, and of course to the pas- 
sage of time. Appropriate boundary circum- 
stances are also readily included. Lateral speed 
of the target, in the air mass, can be set in at 
will, in any direction and to any desired magni- 
tude. 

It has been a simple matter also to include, in 
an independent channel from the control handle 
to the moving reticle, for example, whatever con- 
jectural dynamical relations were proposed for 
effective guiding. Several such systems were 
thus represented. One proposed by the writer 
was shown to be successful, when proper initial 
conditions were observed, in leading to high 
terminal accuracy even in the presence of con- 
siderable target motion in the air mass. The prin- 
cipal point is that means were available, in the 
simulator, to evaluate the excellence or otherwise 
of all the various dynamic proposals which arose 
in development. Such assessment is not practical 
analytically, owing partly to the nonlinearity of 
the systems being studied. Although the reason- 
ing is omitted in this context, it was found ef- 
fective to transmit signals to the bomb controls 
which led them to deflect in proportional response 
to a linear combination of the lead angle, as ob- 


served on the scope or screen, and the rate at 
which the lead angle is changing. The constants 
of such combination depended on the conditions 
prevailing when the operation was begun. Simu- 
lative study showed that such conditions could be 
adequately predicted, that the constants could be 
consequently chosen to suit, and they were hap- 
pily not critical, and that finally the dynamics of 
control suggested led substantially to an inter- 
ception approach by the bomb to the target, un- 
der manual guiding, even in the presence of 
target motion in the air mass. These conclusions 
were later fully confirmed by large-scale tests, 
employing the control dynamics here conjec- 
turally initiated. 

The above dynamic relationship, between the 
lead angle and the instructions to the bomb- 
control deflections were actually embodied, first 
in the simulator and later in the larger equip- 
ment, by insertion of the inverse dynamics, 
essentially a first-order lag, in the connection 
from handle to moving reticle. Thus on the 
assumption that the target is tracked by the 
latter reticle, which thus reproduces the lead, 
and that the handle position directly trans- 
mits the proportional control-deflection orders, 
the dynamic connection from the lead angle to 
the latter deflection, as earlier specified, is ef- 
fected. It is significant that the collision or 
interception approach was made possible in 
this case by a perverse form of ‘‘proportional 
navigation,” without directional stabilization 
or space-rate determination in the missile. This 
was done by interpreting absolute turning of 
the bomb as being caused by the control sur- 
face deflections, which were continuously and 
directly knowable, and as being affected simul- 
taneously and additively by the component of 
gravity, which was predictable through im- 
plicit embodiment in the dynamics of the con- 
trol. A favorable circumstance for this sort of 
trickery, which is more straightforward when 
directional references or absolute angular rate 
meters are available in the vehicle itself, as 
seems signified for the future, a favorable cir- 
cumstance, we repeat, is provided by the ab- 
sence of rapid roll and of pitch and yaw in the 
body of the ROC bomb. This combination of 
properties was not fortuitously obtained, but 
was planned for and designed in. 


SIMULATION OF AIRPLANE DYNAMICS 


63 


In connection with assessment of the miss in 
guiding, meaning the minimum lateral distance 
of the bomb from the target, measured nor- 
mally to the local part of the trajectory, this 
quantity is not easy to measure directly in 
terms of voltages in the simulator. A good 
dodge for this assessment, however, was con- 
ceived and installed in the Columbia Labora- 
tory.*^ The derivative of the angular direction 
of the bomb was determined as seen from the 
target, this angle appearing as a voltage under 
simulation, at an instant when the bomb was 
still a short distance a from the target, and 
had yet t seconds to get there. The ratio a/r 
would be rather well known from the ‘Ter- 
minal” speed Vx of the missile. It is possible, 
thus, to evaluate the miss as the product of 
the square of the remaining range a into the 
above angular rate, divided by the terminal 
speed all these quantities being essentially 
constant, from one trial to the next, except the 
angular rate. Indication of the latter on a me- 
ter, then, provides a sensitive measure of 
error, and a quick and easy means for scoring, 
either in laboratory studies or for training 
purposes. 

Cessation of hostilities brought this project 
to a stopping point in development, but it is 
still planned to prepare an altered version of 
the television bomb simulator for the needs of 
familiarization in the field, in connection pre- 
sumably with guiding trials of the missile 
itself. 

It is considerably to the point, with regard 
to the powers of simulation, that the equip- 
ment described above, through a mere change 
in connections and an alteration of adjust- 
ments, was employed in a stability study of 
underwater torpedo controls. This was pur- 
sued in our laboratories, during a brief in- 
terval, by Section 7.3 following a suggestion 
by the writer that a problem being studied by 
them would be amenable to such simulative 
methods, and that these methods would en- 
compass the nonlinear properties of the con- 
trols, which were the source of some concern. 
The previous analysis had been based on linear 
theory. We mention the application only by 
way of indicating the flexibility of the elec- 

“By L. Julie. 


tronic simulators which have thus come into 
use. It is understood that this particular study 
was satisfactorily concluded. 

4 7 SIMULATION OF AIRPLANE DYNAMICS 

A much more ambitious project,^’® begun 
only recently, was for electronic representa- 
tion of the complex dynamics which obtain 
between the flight controls of the pilot and the 
motions in the air mass of his craft. This work 
was connected with the PUSS project, under 
NO-265, and contemplated the inclusion also 
of simulative components representing the en- 
tire computing sight therein involved. Some 
remarks are made on this score in Sections 
2.1 and 2.8. A fundamental consideration in 
the success of such automatic sights is the na- 
ture of the interactions among the tracking 
system, the computing and display system, and 
the gentleman at the controls. Owing to the 
relative newness of this project, to the fact 
that it is actually part of another project de- 
scribed elsewhere, to the expected continuation 
of this other project together with its simula- 
tive counterparts, and to the fact that a fairly 
complete set of reports have been and are still, 
at the present writing, being submitted by the 
contractor, we shall not discuss this enterprise 
here in any great detail. The simulative tech- 
niques are in no way essentially different from 
those of other projects which have been con- 
sidered, although somewhat greater complex- 
ity was required; and certain refinements re- 
main to be made before the apparatus is finally 
effective. It is now possible, nevertheless, to 
experience “electronic” flight in the laboratory, 
the whole illusion being accomplished by simu- 
lative components between the voltages in- 
curred through motion of the mock controls, 
at one end, and the voltages which deflect the 
spots on scopes to represent target, horizon, 
and sight reticle, at the other end. 

The Bureau of Aeronautics^ Special Devices 
Division was consulted, at the inception of this 
project, in connection with a synthetic trainer 
which was then in development for single- 
seaters, and which surpassed, in the faithful- 
ness of dynamic representation being sought, 
any previous like attempt. This trainer, which 


64 


SIMULATION AS AN AID IN DEVELOPMENT 




was for combat approaches as well as for such 
other difficult operations as carrier landings, 
was to be supplied with a simulative computer 
under development by Ford Instrument Co. 
An ambitious display system was being 
planned for, of only partial interest for our 
purposes, which involved an overhead, inverted 
relief map in color and a periscopic viewing 
arrangement ; extensible, rotatable, tippable 
and translatable. A somewhat complex optical 
system was to have been involved. As to the 
theory of the airplane motions, a workmanlike 
analysis had been prepared at the depot in 
New York® in which coordinate systems for 
unambiguous simulation were worked out in 
great detail. This background was helpful to 
us, partly because such features as coordinate 
systems, and the several transformations these 
systems must undergo in the workings of the 
simulator, form the largest group of technical 
problems thus involved. After commencement 
of the project, little contact was sought with 
this particular Navy agency, since we tended 
as a first approximation toward a less precise 
model, and since a somewhat different co- 
ordinate system was finally settled upon (the 
aerodynamical equations of Sir Melvill Jones 
were taken as standard), but it was planned 
ultimately to join forces when the equipment 
had attained a demonstrable status, since each 
party considered that mutual development 
might be beneficial. On the whole, however, 
BuOrd was dealt with chiefly in this simulative 
venture, rather than BuAer, as being cognizant 
of the more inclusive PUSS project. 

Those parts of the simulative assembly hav- 
ing to do with the operator are enclosed within 
a model cockpit. Thus are included the poten- 
tiometric ‘Yecognizors” of control motions, in- 
cluding stick, rudder, and trim adjustments, 
signal indicators on the instrument panel, and 
a set of three scopes so arranged above as to 
present moving indices on a common focal 
plane, seen in the normal forward direction. 
These scopes carry visual indications of the 
direction to a target on the ground, of the 
altitude of a ‘‘road” passing through the tar- 
get, this feature thus providing a roll-refer- 

®By Seaman Steinhardt, late of the University of 
Vienna. 


ence, and of the cross hairs of a computing- 
sight reticle. 

Approximations are included, in this first 
model, which are based on its use to represent 
either horizontal flight or a more or less direct 
gliding or diving approach toward a target at 
ground level. Plans have been made to allow 
such maneuvers as circling (or “casing”) the 
target, wing-overs as the attack is begun, and 
so on, in future models if such ever are desired. 

The electronic channels of the simulator 
cover circuits in which the lags and inertias of 
the airplane responses, in roll, pitch, and yaw, 
contribute to and characterize the control tran- 
sients; circuits in which the geometry of the 
transformations, from airplane coordinates to 
target coordinates and back again, are accom- 
plished ; and circuits in which are incorporated 
the differential equations at present proposed 
for the PUSS computing system. The chief ap- 
proximation is in the assumed equivalence of 
the sequences, yaw-pitch and pitch-yaw, the 
error of which assumption is not influential 
below roll-angles of 20 degrees or so. By more 
complex circuitry, this approximation could 
be replaced in the simulator by the unapproxi- 
mated circumstance. No new components were 
used beyond those heretofore indicated. All the 
equipment, and there is half a small roomful 
of it, mostly amplifiers, connective electrical 
structures, and regulated supplies, is so de- 
signed that it can be assembled on standard 
relay racks. Present plans are for transporta- 
tion of this apparatus from New York to 
Philadelphia, where it may be used in con- 
tinuation of the Navy Project NO-265, under 
the auspices of a direct BuOrd contract (NOrd 
9644) at The Franklin Institute. 

4 8 POTENTIALITIES FOR THE FUTURE 

Frequently during several of the develop- 
ments above described it has been thought, and 
said, that for the increasingly diversified uses 
to which the simulative methods were being 
put, requiring new construction or at least 
major physical rearrangement of components 
each time, it would be preferable to build an 
extremely general and flexible assembly, cov- 
ering every conceivable type of system, which 


POTENTIALITIES FOR THE FUTURE 


65 


could be adapted to any particular problem 
simply by the manipulation of conveniently 
provided organizational ^‘controls.” Knowledge 
of the means for achieving quite impressive 
generality had gradually been gained, and the 
proposal for such a supersimulator, as it came 
to be denoted, was considered not at all fan- 
tastic. After all, witness the differential ana- 
lyzer. A considerably smaller expenditure 
would provide a machine, albeit less accurate, 
of much greater power in the order of equa- 
tions which could be embodied, and of greater 
flexibility on the time scale. Although a human 
operator may be included as a component in 
a differential analyzer, this is not done in imi- 
tation of a corresponding activity in a situa- 
tion under representation. Thus in guiding 
bombs, for example, the analyzer “dropped” a 
bomb in 15 minutes, whereas in practice it fell 
in 35 seconds. Of course, this is not a perma- 
nent, or inherent, limitation of such machines. 

Although no supersimulator, in the full sense, 
has as yet been prepared, there are many who 
might still be found to be champions of the 


plan, and it would seem to have certain appli- 
cability to future developments in a variety of 
technical fields. 

Certainly flight may be taught by models, at 
least through most of the learning period, and 
electronic simulative techniques will certainly 
be economically superior in this respect. The 
same remark is evidently valid for the special 
flying operations whether by local or by re- 
mote control, of combat conditions. Since the 
equations of rocket flight are not difficult thus 
to simulate, and seeking or remote-guiding 
procedures, manual or automatic, are repre- 
sentable by straightforward extensions of the 
techniques of this chapter, it is evident that 
guided rockets may be studied by such meth- 
ods. Warfare among such missiles could thus 
be staged and observed entirely in the labora- 
tory, possibly with statistical machinery in at- 
tendance for interpretation and assessment. 
Years of experience, and of trial and error, 
on the development of controls and dynamic 
components could thus be collapsed into hours. 
There is, in reality, no limit at all. 


CQIS^^IDENTIAL 


Chapter 5 


LINKAGES FOR COMPUTATION AND MANIPULATION 


5 ^ GENERAL TYPE CONSIDERED 

A/TECHANICAL LINKAGES and the operations 
they perform are of permanent interest to 
the geometer, who finds them irresistibly fas- 
cinating, and they hold attraction, in addition, 
for the analyst who sees recondite real functions, 
perhaps of several variables, come to life in his 
hands. Throughout this discussion we refer to 
linkages in the purest form, in two or three 
dimensions, meaning thereby those linkages 
which consist in assemblies of moving parts 
which are joined at points or lines only, having 
no rubbing or rolling except in the neighborhood 
of such point or lines, that is to say only at true 
bearings. The so-called friction radii are thus 
very short in comparison to the size of the as- 
sembly. While we wish to speak principally of 
this class of mechanism, and may expound the 
advantages therein for certain purposes, this is 
by no means to detract from the benefits, in com- 
putation or otherwise, of other classes which may 
be named. Thus cams, either flat or three-dimen- 
sional, have natural applications and need fear 
no competition from linkages in such fields. Cams 
are important, and we have made use of them ; 
our indifference as expressed by the omission of 
cams from these pages means simply that they 
are adequately treated elsewhere, or rather that 
we have nothing new to offer on the subject. The 
same is chiefly true of computational devices in- 
volving other means than linkages for the em- 
bodiment of their laws of operation, although 
other sections of the present report may be 
found to be obsessed, for example, with electri- 
cal computers (Chapter 10). 

Linkages with sliding joints are not primarily 
discussed here, although there is thus included 
an extremely broad group, and such may occur 
in combination with the forms having nonexten- 
sible members. Sliding linkage is useful in many 
computations of partially geometric nature, for 
example, and the frictional forces may in some 
certain cases be made extremely small through 


designs which involve pins of small diameter. Our 
primary interest has been in relatively small 
linkages, of light weight and high resistance to 
the ills of vibration and unbalance, very low in 
the input torques required to manipulate them, 
and offering flexibility in adjustment and mod- 
ification. The exclusive use of pivots in the design 
of such components has become a policy rather 
than a rigid rule. It is felt, however, that this 
policy has paid well for the effort given to pro- 
moting it. 

We wish to state in general that we have some 
little knowledge, but no more than that, of link- 
age developments elsewhere.*'^ We understand 
that our philosophy of linkages is independently 
shared by such workers, whose proficiency may, 
incidentally, date back considerably before our 
own efforts. It is not known whether any other 
activities have led to components as small as ours, 
where a 2-inch link is a lengthy one. Linkages of 
this size are far from unusual in such aircraft 
instruments as altimeters, and our computers 
were physically similar to these in some cases, 
but naturally of an entirely different order of 
complexity and of adaptability in the mathe- 
matical functions they embodied. We shall thus 
speak of our own developments as though no oth- 
ers existed, although thereby we may inadver- 
tently give the impression, to a better instructed 
perusal, of unwarranted claims to novelty. No 
such unestablished claim, however, is intended. 

Admittedly many of the advantages attached 
to pivotally constrained linkages are practical 
ones, depending on the developed techniques of 
design and construction. It is easier for example 
to obtain, from a typical design department and 
shop, a good bearing than a good sliding joint. 
This is more than a mere matter of tolerances, 
but depends rather on the familiarity of tech- 
niques, and on the available tools for their appli- 
cation. Furthermore, for a certain category of 
purposes, where only small angular motions are 

“By Svoboda, el al., at MIT Radiation Laboratory, for 
example. 



66 


METHODS OF DEVELOPMENT 


67 


needed, this type of linkage generalizes quite 
nicely to flexure joints, which have many addi- 
tional charms. It is held that the problems of wear 
and dirtiness, from the important standpoint of 
maintenance, are considerably simplified in 
mechanisms of this general type. 

5 2 METHODS OF DEVELOPMENT 

We shall deal here very sketchily, if at all, 
with standard pedagogic descriptions or with the 
theory of well-known linkage designs. The four- 
bar linkage, so-called, or the four-link mecha- 
nism, which receives its name, remarkably 
enough, from the three moving members it in- 
volves, must be mentioned as the most funda- 
mental component of the class considered. For 
some reason the flat, or two-dimensional, form 
is the only one widely used for computing pur- 
poses, where the nature of the functions em- 
bodied is important. Three-dimensional four- 
bar linkages are used predominantly for ma- 
nipulative purposes, and less frequently, in 
typically approximate circumstances, to achieve 
a ‘"characteristic.” We shall refer only to the 
flat form hereof. And throughout we consider 
all linkages as being interposed, chiefly, be- 
tween angular rotations as input and output, 
more than one of each, in general, being 
involved. 

A basic four-bar linkage is shown in Figure 1. 
This component is extremely flexible, although 
it yields somewhat grudgingly to analysis. Al- 
though it is simple enough to write equations for 
this linkage, the determination of the three 
parameters, for example of the relative link 
lengths, to fit a desired characteristic is not 
direct by that method. Geometric criteria are 
found more suitable, and a number of these are 
available. Thus it is known, for example, that 
the derivative of one of the principal angles, 
6^ and 6^, as shown, with respect to the other, 
say dejde^, is a function only of the position 
of the intersection between the line joining 
the fixed pivots and that of the free link, and is 
in fact equal to the ratio of the distances 
from the fixed pivots to such intersection. 
A useful design criterion is hereby provided, 
determining the local slope of the connecting 
relation between 6-^ and considered as 


plotted*^ against one another in rectangular 
coordinates. Having three parameters, a bit of 
geometry leads to adjustments which may fit 
three points on the curve, or two points and the 
slope at one, and so on. Functions of one variable 
which are not too badly behaved may be incor- 
porated this way, almost to an arbitrary preci- 
sion, since it is possible to connect such linkages 
in a chain, the input of one driving the output of 
the next, obtaining thus 3n adjustable param- 
eters, plus initial conditions. In the simple four- 
bar linkage there are numerous interesting spe- 
cial cases. Either or both angles may be re- 
stricted to less than complete cyclic rotation, 



whereas periodicity of other types may also be 
present. For relatively close fixed pivots, both 
angles may rotate through 360 degrees, leading 
to many useful transformations in cyclic ma- 
chinery and computers. In exploring the pos- 
sibilities of such linkages, to perform a certain 
angular transformation, one may proceed by 
choosing a set of values, say equally spaced, for 
one of the angles, and assign the set of values, 
for the other angle, which correspond individu- 
ally to the first set under the desired transfor- 

‘’An earlier stratagem involved building an experi- 
mental linkage 'with adjustable members, 'with the t'wo 
angles driving a recording stylus linearly on an adjacent 
rectilinear plot. The desired function being first dra'wn, 
the lengths are adjustable for a best compromise. 


-NFIDENTIAL 




68 


LINKAGES FOR COMPUTATION AND MANIPULATION 


mation. Laying out the first set as points on 
an arc of arbitrary radius, choose successive 
constant lengths and draw complete circles 
about each point with radii all corresponding 
to one such length. If exploration of the pat- 
tern formed by the circles having radii equal to 
one such length does not disclose division of a 
superimposed arc in accordance with the trans- 
formed point-set, then one may try another con- 
stant length for the radii, and so on. One is thus 



Figure 2. Geometrical development for linkage. 


exploring a very broad field, but for reasonable 
precision it is surprising to find a case where the 
process fails to produce quickly a workable link- 
age. Figure 2 is intended to show the procedure 
thus briefly described. Approximations have 
been made, using such linkages in computing 
mechanisms, which have satisfactorily repro- 
duced such simple functions as reciprocals, 
squares, and consequently of course, by reversal, 
square roots, and so on ; but the typical applica- 
tion is to correct for some empirical distortion in 
associated equipment, or to embody a law which 
has been determined experimentally in response 
to the functional contributions of several com- 
ponents in a given system. 


Counterbalancing of four-bar linkages may be 
essential where the input power is low, although 
under such circumstances this problem is largely 
conquered by making the members light and the 
inertias low. If each terminal link carries a count- 
erweight whereby it is independently in static 
balance, then to each such counterweight may be 
added what is necessary to balance half the 
weight of the free link, considered of course at 
the appropriate moment arm. The problems of 
such balancing are n-fold if the computer is to 
work under ng acceleration. For the more intri- 
cate linkage assemblies, the problem of balance 
becomes correspondingly so, in accordance with 
some power of the number of connected free 
links, and here approximations will frequently 
suffice, using counterweights on the terminal 
links only, calibrated to resist accelerations un- 
der some chosen average condition of all inputs. 

The typical function of two variables which 
appears in connection with airborne aiming-con- 
trol computations, may be synthesized to a sur- 
prising accuracy by means of the simple 6-mem- 



Figure 3. Typical linkage for function of two variables. 


ber (we depart from the classical nomenclature) 
linkage as shown in Figure 3. An attempt is 
made, in Figure 4, to portray the general plan 
whereby such linkages may be developed. One 
begins with a parametric plot, say in linear and 




METHODS OF DEVELOPMENT 


69 


rectangular coordinates, having a set of curves 
of which each corresponds to a value of the third 
variable, the other two being on the coordinate 
axes. Now it is immaterial which of these vari- 



Figure 4. Development of linkage such as shown in 
Figure 3. 

ables is the dependent one. It is only necessary 
that when two definite values are assigned for 
any two of the variables, that only one significant 
value appear, on the graph, of the third. Some 
multivalued functions may be thus represented, 
as when the input or output motions are cyclic, 
but we shall consider only the simpler cases, 
which indeed have found greatest application. 
One begins, as we have said, with a normal para- 
metric plot. The number of parametric curves 
depends on the precision specified, and on the 
regularity of the function over the field, or more 
precisely on the ability to interpolate. Suppose 
six curves are sufficient, as in our cases has al- 
ways been adequate. The next step is to choose 
six representative values of each coordinate, in- 
cluding the maximum and minimum to be con- 
sidered in each case, and to draw in the corre- 


sponding coordinate rulings, specially designated 
in some way, as by heavier rulings. We have thus 
a network, as shown in the inset of Figure 4, rep- 
resenting a skeleton, so to speak, of the func- 
tional relation to be mechanized. The problem 
now is to perform conjectural warpings of this 
network, in which all intersections and relative 
positions are preserved, until one is obtained, if 
indeed it can be, which meets certain qualifica- 
tions. The magnitude of this task, which is bet- 
ter demonstrated at first hand than explained 
thus in literary fashion, depends principally 
on the nature and consistency of the set of 
parametric curves of the network or original 
plot. Choosing, say, the network of rectangular 
coordinates initially, one replaces these by arcs 
of circles, in the case of each coordinate, of in- 
variable radius and having their centers them- 
selves on the arc of a single circle. For each 
coordinate, then, there is a center belonging 
thereto, an arc about such center with points 
appearing thereon, disposed according to the 
angular functional representation desired for 
that input or output of the linkage. About each 
such latter point is described one coordinate 
arc of the transformed network. The two sets 
of coordinate rulings have now become, con- 
jecturally, two families of circular arcs. On 
this network the parametric curves are now 
redrawn, changed in general shape but faith- 
fully retaining their intersections with the co- 
ordinate network. Smoothing processes, by es- 
timation or through more meticulous geom- 
etry, may be employed in completing the net- 
work by the addition of the new parametric 
curves. If the parametric curves were smooth 
and regular in the original plot, or network, 
they will generally remain smooth in the trans- 
formed one. Frequently it is sufficient to show 
only the intersection points of these curves 
with the new coordinates, appropriately sym- 
bolized to identify the individual members of 
the family. Now comes the test. Do the trans- 
formed parametric curves appear as arcs of 
circles? If not, try a new transformation. This 
trial process is not tedious, after some prac- 
tice, and a bit of experience shows how to 
plan each successive trial to come nearer the 
desired result. If the transformed parametric 
curves are arcs of circles but each arc has a 


)NFIDENTIAL 




70 


LINKAGES FOR COMPUTATION AND MANIPULATION 


different radius, we must still retransform, but 
this is commonly not difficult, since by a re- 
location of pivot points the required additional 
warping may be fulfilled. Suppose that finally 
the desired condition is obtained; all curves, 
coordinate and parametric, are arcs of circles. 
There is one more criterion, but fortunately 
this tends almost always to be automatically 
satisfied, to reasonable precision. The centers 
of the arcs of equal curvature, which are the 
transformed parametric curves of the original 
plot, should lie on the arc of a circle. Now this 
circle may have a very large radius, and thus 
may be nearly a straight line. In such cases, 
as when also the locus of centers is a curve 
pronouncedly differing from a circle, further 
alteration of the coordinate transformation 
may help. By this time however, so many con- 
ditions have been met that one may not expect 
much further freedom, and it is best, as, for 
example, in the straight line locus, to add a 
few links so that the linear motion may be 
converted to rotary, without the use of inor- 
dinate radius arms, through a Watts linkage 
or other simple and approximate linear mo- 
tion: here used backwards. Similarly, any out- 
put (or input) function, as it must appear in 
the linkage developed as above, may be trans- 
formed uniquely so as to alter the calibration 
there presented. Four-bar linkages, either sin- 
gly or in series, may be applied here. Thus we 
may want a linear or a reciprocal calibration 
of any of the associated variables, and we may 
have it, no matter what internal calibration 
was required for the linkage design as such. 

If graphical functions resist such represen- 
tation, it may be advisable to replot and pro- 
ceed again, replacing one coordinate by the 
parametric variable. In spite of such trickery, 
and of the free play of imagination in framing 
linkages, certain functions may remain refrac- 
tory. We have not met any as yet. For exam- 
ple, when the parametric curves of the origi- 
nal plot cross one another, and overlap even 
considerably, this is not fatal at all, but yields 
directly to the above method. Further measures 
may be applied also, if part of a parametric 
family is warped in some local fashion, for 
linkage components may modify the output; 
and numerous generalizations are possible on 


the above-mentioned components, each having 
its peculiar powers for representation. It is 
safe to say that any systematic function of 
physical significance may be embodied, to any 
desired excellence of approximation, in link- 
ages of this general type. 

5 3 MORE COMPLEX FUNCTIONS 

In passing from functions of two variables 
to functions of three, and thinking of linkage 
representation, we pause to note that the prop- 
erties of all functions which make them easy 
to represent are definitely not the properties 
of mathematical simplicity. Better criteria 
would be expressible in terms of graphical con- 
figuration. Paradoxically, it is easier to make 
a multiplier, = xy^ than an adder, z = x -[-yj 
by the methods outlined above. Even brief ac- 
quaintanceship with such development gives 
the facility for predicting the representability 
in linkage of a set of graphical data. 

We note further the tendency to make theo- 
retically exact computers, which has led to 
much heavy machinery, whereas in general 
the precision of computers is far greater than 
that of other components or processes in sur- 
rounding equipment. It is gathered that equal 
effectiveness might have been gained more eco- 
nomically, in many such cases, through the use 
of simpler and lighter, albeit yer se less pre- 
cise, pivotal linkages for computation. 

The incorporation in linkage of a function 
of three variables represents in general a big- 
ger step, as compared to the case of a function 
of two variables, than does the two-variable 
case in comparison to that of a function of one 
variable. For many such problems which arise 
in practice, however, the task is simpler than 
might thus be indicated, owing to the tendency 
of engineering functions toward reasonable be- 
havior. By canny choice of the variables to be 
considered in sequence, and of the sequence 
itself, one may frequently generalize from a 
linkage for functions of two variables to the 
complete linkage for three. For example, if the 
three-variable function may be considered a 
function of (1) one of the three variables and 
(2) another function of the other two varia- 
bles, then the whole problem is simply solved 


SOME APPLICATIONS 


71 


by twice applying the above technique for func- 
tions of two variables. An example of such a 
linkage, for computing a function of three 
variables, is shown in Figure 5. The criterion 



for such reduction of a function f(x,y,z) is 
that, to a sufficient approximation 

f(x,y,z) = g{h(x,y),z). 

First a linkage would compute h from x and y 
as inputs, and then g and consequently / from 
h and 2 : as inputs. An elementary example of 
such specialization is provided where / may 
have a factor involving only one of the varia- 
bles, as when 

z 

J{x,y,z) = z<t>(x,y) =7 / {x,y,Zi) . 

The class of all functions for which the first 
named reduction is possible is apparently not 
easy to define more specifically ; the question of 
such reducibility is evidently not mathemati- 
cally trivial. When functions are not amenable 
to such treatment, however, linkages may still 
frequently be made by using this process as a 


guide, ^'expanding around’^ some central con- 
dition, as it were, and approaching the desired 
precision by a process reminiscent of successive 
approximations. 

A somewhat less restricting property which 
allows representation, on the basis of the ear- 
lier method, is that the function be separable as 

fix,y,z) = F{u{x,y),v{y,z)) , 

for example, and it is claimed^ that linkage de- 
sign may be based on functional considerations 
even more general than this. The design cri- 
terion, it should be noted, of the number of 
links required in any particular case, is of less 
importance, for example, than the local com- 
pression of the output scales, which may lead 
to errors in the presence of lost motion, or to 
additional difficulties in obtaining a more de- 
sirable calibration. 

Generally speaking, it is characteristic of the 
procedures of mechanization wherein compu- 
tation by linkage is involved, to omit the step 
in which empirical formulas are developed to 
fit certain data which must be embodied, and 
to pass directly from such data, presented in 
graphical form, to the computing linkage itself. 
In many cases, where this procedure is legiti- 
mate, a large saving in time and effort may be 
realized. 

s ^ SOME APPLICATIONS 

There have been several occasions for apply- 
ing linkage computers, of the above general 
type, in the design of fire-control systems for 
airborne torpedoing and bombing, where par- 
ticularly it has been desired to prepare com- 
ponents which would fit into extremely small 
space. Such drastic restrictions on space arose 
either because the equipment was to be squeezed 
into positions which were already crowded by 
other necessaries, as in the case of the de- 
velopment which resulted in the torpedo di- 
rector Mark 32, or because the major assembly 
was to be hand held by the operator, as were 
the developmental models of the project ter- 
minating in the bombsights Mark 20 and Mark 
24. Further need has been present for mecha- 
nization in this form since, for similar reasons 

‘'By E. Elyash of The Franklin Institute. 




72 


LINKAGES FOR COMPUTATION AND MANIPULATION 


again, a minimum power load for operation 
was desired. Finally, it was held, and this is 
as true as ever, that linkage construction lent 
itself well to mass production techniques as 
represented in the facilities of the manufac- 
turer not ordinarily practicing in the fire- 
control field. 

A relatively simple case in which such a link- 
age was forced into service with evident bene- 
fit was in connection with a guided bomb simu- 
lator, where in production it was found diffi- 
cult to procure potentiometers having a square 
law in resistance versus rotation. Several such 
units, ganged, were to be involved in each pro- 
duction unit. It was made possible to use the 
commoner linear potentiometers by driving 
them through an inexpensive linkage which 
approximated the square law remarkably well. 
In this case completely cyclic operation was 
also required. There may certainly be many 
such cases. The most serious applications of 
such methods of computation, however, oc- 
curred in the development of aiming controls 
for rocketry and for toss bombing. There was 
PARS, for example, an ambitious project for 
the construction of a miniature rocket sight.** 
In this instance the plan was to include the 
whole system, except for the pilot’s sighting 
index itself, within the case of an aircraft 
altimeter, barometric altitude being one of the 
inputs. Indicated airspeed, normal accelera- 
tion, and temperature, were also inputs and 
were also locally supplied, all inputs taking 
the form of (angular) motion. A quite small, 
fiat linkage, of the type described, computed 
the '"super-elevation” as output from the above 
input motions. This project led to an experi- 
mental model and to preliminary tests, but is 
not considered to be finished, or to have re- 
sulted as yet in a completely workable system. 

In the PUSS project there has been the most 
thoroughgoing employment of all-pivot link- 
ages with which we have been connected. In the 
computing component of the aiming-control 
system involved here, a multipurpose linkage 
serves in connection with the rocketry and 
tossing bombing functions. The linkage com- 
puter, employed as a "static” computer, as we 

^Pursued on a developmental and design level, prin- 
cipally between H. Whitney of AMG-C and R. W. 
Pitman of The Franklin Institute. 


may say since time is not explicitly there in- 
volved, is connected intimately with the com- 
ponents of the dynamic computer, the form of 
which differs in the various versions, pneu- 
matic and electric, which are being experi- 
mentally prepared. To the amalgamated link- 
age go eight inputs, two of which are manu- 
ally effected and the rest automatically. Four 
outputs are derived, setting parameters in the 
dynamic computer and, in one case, determin- 
ing a release condition. Most of the inputs 
apply at several places in the linkage assembly, 
being joined mechanically then by common 
shafts, and several intermediate computations 
are performed internally. The design of the 
latest experimental form is in four layers, 
being mounted on a framework involving cor- 
respondingly many plates. This present design 
is to fit into a 6-inch cube, complete with coun- 
terbalances, etc. Approximately five dozen 
individual links are contained. 

5 5 A THREE-DIMENSIONAL LINKAGE 

We shall speak next of a particular type of 
linkage as an element of mechanism, first quite 
aside from its potentialities for usefulness. It 
was initially^ demonstrated in this connection 
by the waiter, however, as the exact solution 
to a problem of so moving a mirror as to give 
a certain desired behavior of the reflected ray. 
As soon as the linkage was proposed, however, 
it was recognized that it had properties of sev- 
eral different sorts, suggesting a number of 
other applications, and that furthermore it 
appeared to be geometrically fundamental and 
thus to warrant existence in its own right. 

The linkage thus lavishly introduced involves 
five linear pivots, or hinges, by which its mov- 
ing members are joined, there being no slid- 
ing or rolling connections aside from the bear- 
ings or hinges thus included. While there are 
many possible variants, the basic linkage may 
be defined most readily in terms of the rela- 
tions among the axes, each possessed in com- 
mon by two members or links of the linkage, 
of the hinges or bearings. A complete defini- 

®As to originality, this is evidently disputable since 
E. L. Rose has remarked that a similar structure was 
arrived a^: by E. Root III for some mathematical func- 
tion, using the reasoning of projective geometry. 


A THREE-DIMENSIONAL LINKAGE 


73 


tion is supplied by the statement that, in the 
linkage, each of the five such axes, all five 
being concurrent or having a common point of 
intersection, is maintained perpendicular to 
each of two others. It is the function of the 
joining links, of course, and we include the 
‘^stationary” link as in the term four-bar link- 
age, to maintain the orthogonality between the 
axis pairs. An equivalent statement, which 
may seem at first paradoxically so, is that there 
are five concurrent axes which may be consid- 
ered in a “ring,” each being perpendicular to 
the next in the ring. It is, incidentally, rather 
interesting to consider the special cases, for 
axes having this type of mutual orthogonality, 
for four axes and for three. The present link- 
ages reduce to these by application of certain 
constraints, as may be expected. In recognition 
of the numerical and angular properties of the 
hinge axes in this linkage, it has been called 
the orthopentax. 

An axis held in double gimbals of the well- 
known type is a three-dimensional generaliza- 
tion of a simple two-dimensional hinge. It is, 
however, an asymmetrical such generalization, 
since one input axis is carried along when ro- 
tation about the other is introduced. The. or- 
thopentax is a symmetrical such generaliza- 
tion, both input axes, in the generation of a 
doubly hinged and spatially moving output 
axis, remaining stationary. 

In Figure 6 is illustrated an elementary form 
of the orthopentax linkage, displayed in three 
typical conditions. In the particular form here 
shown it is seen that there are four movable, 
right-angle links, two of which pivot in sta- 
tionary bearings and the remaining two of 
which pivot in bearings which are fixed in the 
first pair of links, the second pair joining one 
another in a fifth bearing. The axes of the five 
bearings are the five axes referred to above. 
If the shaft affixed to the fifth bearing, in the 
center of the linkage, be regarded as a manipu- 
lable gnomon, or index in space, its motion, 
under applied rotations of the terminal links 
about the stationary axes, is of interest. For 
consider the parallel projections of the gnomon 
on each of two planes which are normal to the 
stationary axes. It will be recognized that the 
rotation of each such projection of the gnomon 


is precisely equivalent to the input rotation of 
the corresponding terminal link about its sta- 
tionary axis, and is completely unaffected by 
the input rotation of the other terminal link 
about the other stationary axis. 

If we imagine a sphere of any radius, cen- 
tered in the common intersection of the axes 
of the orthopentax, then the locus of the pierc- 



Figure 6. Fundamental three-dimensional linkage; so- 
called orthopentax. 

ing point of the extended gnomon in the sur- 
face of this sphere, on rotation of the terminal 
links, has special properties. If either terminal 
link is unrotated, then rotation of the other 
link causes the gnomon to trace a great circle 
on the surface of the sphere. All such great 
circles intersect in two poles which are them- 
selves the two intersections of the stationary 
axis, of the unrotated terminal link, with the 
sphere. There is thus established on the sphere 
a coordinate system given by the network of 
two families of great circles, each having a 
pair of poles in common, and the two pairs of 





74 


LINKAGES FOR COMPUTATION AND MANIPULATION 


poles perpendicularly disposed on the surface 
of the sphere. The corresponding coordinate 
systems for a double-gimbal arrangement is 
similar to that of latitude and longitude, con- 
sisting in polar great circles and zonal circles ; 
it is an orthogonal system on the sphere. 

Again, if one considers the intersection of 
the gnomon of the orthopentax with a plane 
parallel to the plane of the two stationary axes, 
it is seen that this intersection follows straight- 
line loci when the individual terminal links 
are manipulated. The coordinate system thus 
formed is orthogonal, and is linear in the tan- 
gents of the angular rotations of the terminal 
links out of their zero positions, which latter 
correspond to normality between the gnomon 
and the plane of projection. This property of 
the orthopentax linkage implies significance 
for many special applications, where independ- 
ence and symmetry of the two modes of 
manipulation is important in the generation 
of a direction in space. 

To avoid misunderstanding, it must be 
pointed out that a geometrical similarity may 
be shown between the function of the ortho- 
pentax and the combination of a double gimbal 
system and a so-called hail ring. In the latter 
combination, however, one of the projected an- 
gles does not appear explicitly, in tangible form 
for indicative purposes or other employment 
that is, and furthermore either sliding or roll- 
ing must be resorted to in a mechanical guide, 
rather than the exclusive application of purely 
pivotal bearings, as in the orthopentactical 
linkage. 

s ^ MANIPULATION OF A MIRROR 

In connection with the presentation to a pilot 
of the output of an aiming control system, in 
the form of a reticle image, which image is to 
be made to coincide as aiming criterion with 
the target direction, it is desired to produce 
such an image by reflecting, from a single 
moving mirror, the parallel light rays from a 
collimator which is stationary in the fighter 
airplane. It is desired further that the depar- 
ture of the reticle image, which actually is seen 
by the pilot after reflection from a sloped and 
semitransparent surface before him, from a 


zero position approximately straight ahead, 
shall be under the symmetrical control of two 
deflection variables so that these variables pro- 
duce rectangular motion of the apparent posi- 
tion of the reticle on an imaginary plane nor- 
mal to the zero direction and having rectangu- 
lar axes along the airplane’s "‘horizontal” and 
“vertical.” For constructional convenience it 
is planned that the normal or neutral position 
of the moving mirror be at 45 degrees, say, to 
the incident and reflected beams. These re- 
quirements are similar to those which arose in 
connection with the so-called Project PUSH 
(Chapter 10), for a pilot’s universal sight 
head, within the more general PUSS project. 

It became recognized that the problem, 
namely that of preparing a linkage to move 
a single mirror in the manner prescribed, can 
be broken into two subsidiary problems, first 
to so manipulate a mirror that the reflected 
ray was along the direction of a single manipu- 
lating rod, and second to direct the latter rod, 
in response to two input rotations, in the man- 
ner desired for the reflected ray, or, what is 
tantamount to the same thing, for the image 
of the reticle. Now the first such component 
projblem is answered by an astronomical mech- 
anism known as Foucault's siderostat, which 
had been used to reflect continuously the image 
of a star into a stationary camera. The second 
component problem is solved by a direct ap- 
plication of the orthopentax linkage. This view 
of the overall solution was not suddenly con- 
jured up, a good deal more groping having 
been involved than might hereby be indicated, 
but it is true that division of the problem in 
this manner was appropriate as soon as the 
general form of the answer was once seen. 

The siderostat already referred to involves 
a slanting mirror held in a double gimbal, the 
stationary axis whereof is along the fixed ray 
to, or from, the mirror. The mirror rotates 
about an axis in the “outer” gimbal, which lat- 
ter axis is normal to the stationary axis of 
the gimbal. A link mounted as “inner” gim- 
bal on the first gimbal, and having an axis in 
the latter parallel to that of the mirror, car- 
ries a fixed rod perpendicular to the latter 
parallel axes and in its neutral position normal 
also to the stationary axis of the first gimbal. 


MANIPULATION OF A MIRROR 


70 


Then by so connecting the rotations of the in- 
ner gimbal and the mirror, as by the well- 
known half-angle linkage, so that the mirror 
rotates, with respect to the outer gimbal, half 
as fast as does the inner gimbal, the reflected 
ray or beam may be made to coincide identi- 
cally, under all conditions of manipulation, in 
direction with that of the said rod. 

It remains merely to employ the orthopen- 
tax linkage for the manipulation of the direc- 
tion-determining free rod. In such employment, 
parts of the normal orthopentax combine natu- 
rally with parts of the siderostat, so that the 





Figure 7. Orthopentax as mirror manipulator for 
oblique incidence. 

resulting assembly, as shown in Figure 7, is 
not simply the sum of the two component mech- 
anisms, and indeed can be justifled by less 
roundabout, albeit somewhat more special, ar- 
guments. The arrangement shown in the latter 


flgure is based on the alternative position of 
the purer linkage shown in Figure 6C. For 
small angular departure of the reflected beam 
from the neutral, the projective orthogonality. 



Figure 8. Orthopentax as mirror manipulator for 
obhque incidence; same as Figure 7, but for normal 
incidence at neutral. 

which is exactly embodied in the linkage al- 
ready described, may be preserved to a re- 
markable approximation by omission of the 
half-angle mechanism. The somewhat simpler 
method of mounting the mirror on the inner 
gimbal, which is thus permitted, is shown by 
the inset in Figure 7. Many other variants are 
possible. Another exact method of manipula- 
tion, when it is desired that the incident and 
reflected beams be parallel in the neutral case, 
for zero deflection, is shown in Figure 8. Here 




76 


LINKAGES FOR COMPUTATION AND MANIPULATION 


a three-dimensional form of the half -angle link- 
age is applied, by displacing equally the centers 
of the mirror linkage and the free bearing of 
the orthopentax (cf. Figure 6A) from the 
plane of the stationary axes of the latter 
linkage. 

One property of such manipulations, involv- 
ing only one mirror, is that of rotating the re- 
flected image about the axis of the reflected 
beam, as manipulation takes place. If this is 
objectionable, one must then resort to more 
than one mirror or to corrective rotation of 
the primary image-forming pattern. 

5 7 TRIGONOMETRIC COMPUTATIONS 

Many broadly inclusive geometric and trigo- 
nometric functions are embodied among special 
lines in a rectangular octant. Consider thus one 
such octant, or the corner enclosed among three 
perpendicularly intersecting planes, and sup- 
pose lines are allowed to move, one in each of 
two of the planes, so that they pass always 
through the triple point of planar intersection. 
These two lines, each of which is perpetually 
perpendicular to one of the coordinate axes 
formed by the figure, may coincide with one 
another as a special case in the third such co- 
ordinate axis. Let us consider the angles be- 
tween each such line and the said third coordi- 
nate axis, these angles being both zero when 
the two lines coincide, and each angle having 
values between plus and minus one right angle. 
Consider further, in each of the two planes to 
which the above lines are restricted, second 
lines each perpendicular to the first lines. We 
now ask: what is the angle between these sec- 
ond lines? It is not difficult to show that this 
is the angle of which the cosine is the product 
of the sines of the two angles first introduced 
for the rotating lines. Consequently the sine 
of the departure from a right angle of the angle 
between the second lines is the product of the 
sines of the two input angles. Now by refer- 
ence to Figure 6 it may be seen that the above 
geometry is completely embodied in the ortho- 
pentax linkage. The final angle, of course, cor- 
responds to that between the two free links, 
and describes their relative rotation about the 
gnomon. There is thus tangibly afforded a pre- 


cision method for the multiplication in terms 
of the sines of angles, and consequently of such 
other operations as those involving ratios in- 
stead of products, by an inverse operation, or 
cosines rather than sines, through readily 
applied alterations of the procedure. 

To return for a moment to the geometrical 
picture already employed by way of clarification, 
one may wonder why the angle directly between 
the lines originally introduced was not employed, 
rather than that between the lines perpendicular 
to and respectively coplanar with the originally 
introduced ones. Well, this is not hard to ex- 
plain in terms of mechanism. Consider what 
mechanical contrivance would be required to 
maintain indication as the latter lines passed 
through coincidence, their included angle then 
passing through zero and changing sign. Thus, 
although the sine multiplication may certainly 
be carried out between these original lines, or 
with the corresponding linkage, which might be 
entirely different from the orthopentax, their re- 
placement by the perpendicular references, or 
the journey twice “around the comer” as in the 
orthopentax, avoids the embarrassing circum- 
stances in the neutral position, and makes a 
simply constructed all-pivot linkage do the com- 
putation perfectly. For some applications, of 
course, the mechanical embodiment of an im- 
portant variable in the relative rotation of a 
bearing which has such positional freedom may 
be highly objectionable, and may invalidate the 
appropriateness of the method. The methods for 
removal of such apparent disadvantages, and, 
for that matter, the remaining computational 
potentialities of the orthopentax linkage have 
not been exhaustively explored. 

5 « OTHER FUNCTIONS AND FORMS 

Owing presumably to the fundamental char- 
acter of the orthopentax linkage, a number of 
interesting applications have been discovered 
to widely diverse fields. Many such applications, 
all of which incidentally cannot be here given in 
any detail, stem from the appropriateness of 
this linkage as a general deflector in space, 
whereby two input rotations, with respect to 
stationary bearings in a rigid framework, are 
permitted symmetrically to manipulate and 




OTHER FUNCTIONS AND FORMS 


77 


uniquely to determine the direction of an index 
member. In this sense the linkage may be 
thought of as a modified universal joint, and 
has other properties which may be inferred 
from the latter type of function. 

If the free index, or gnomon, of the ortho- 
pen tax (Figure 6) be constrained to rotate in 
a plane pei’pendicular to that of the two sta- 
tionary axes (as may be accomplished by in- 
clusion on the index member of a second bear- 
ing or pivot which permits rotation about a new 
stationary axis lying in the latter plane, and 
which is perpendicular to the original bearing 
axis of the index) , then rotation of either orig- 
inal terminal link about its stationary axis re- 
sults in a corresponding rotation of the other 
terminal link. The correspondence is one of 
equality when the plane of constraint referred 
to is normal to the bisector of the original sta- 
tionary axes. Thus is formed a right-angle drive 
without gears, or a universal joint with uniform 
rotational properties, if such is desired. The 
freedom of rotation, however, of either input or 
output, that is to say of the terminal links, is 
necessarily limited to something under 360 de- 
grees, owing to blocking action of the com- 
ponent links. For small rotations of both input 
and output, a torque amplifier results. Unity 
gain corresponds to the case latterly mentioned, 
when the plane of constraint is symmetrically 
placed with respect to the stationary axes, or 
when the new stationary axis, about which the 
gnomon member must rotate, bisects the orig- 
inal stationary axes. If, however, the new bear- 
ing axis is itself rotated, in the plane of the 
stationary axes, and is maintained concurrent 
with these and all the other axes, then any 
transmission ratio of torque from nearly zero 
to nearly infinite may be selected at will. This 
should provide a large improvement over levers. 
Some simpler forms, of such a torque multiplier, 
may be derived for special applications. 

The orthopentax has a further most surpris- 
ing property which may be illustrated by assum- 
ing that a source of torque is available, with 
respect to the framework, for application about 
the gnomon or index axis to the two links 
hinged therein, both such torques having 
strengths independent of the angular motion 
of each such link. Figure 6A may be referred 


to, for example, in this demonstration. Under 
the application of the torques, it is evident that 
in the neutral position corresponding to what 
we may call the zero position of rotation of the 
terminal links, when the gnomon axis is normal 
to the plane of the stationary axes, no result- 
ing torques will appear on the terminal links, or 
about the stationary axes. When, however, 
either terminal link is rotated from its zero 
position, as above agreed upon, a torque will 
appear on the other terminal link, about its 
(stationary) axis, since a component of the full 
applied torque is then allowed to exert itself 
there by the rotation imposed. This inverse re- 
lation holds simultanously in both directions, 
from each input rotation to the corresponding 
torque about the other axis, and the relation is 
undamaged when both rotations take place to- 
gether. Such resulting torques are proportional 
to the sines of the corresponding rotations, and 
of course also the magnitude of the full 
torques originally applied. We have thus the 
spectacle of a pair of springs, so to speak, the 
reaction of each depending uniquely on the de- 
flection of the other. It is not known what ap- 
plications this may have in general, but one 
such application, which was seriously consid- 
ered, has been to the implicit stabilization of a 
semiconstrained gyro system. Recall that a gyro 
normally spring-constrained in gimbals will nu- 
tate badly. Consider thus a symmetrical gimbal 
formed from an orthopentax, with the gnomon 
coinciding with the gyro rotoFs axis. Now let 
the round-the-corner rate versus torque charac- 
teristic of the gyro be matched by the corre- 
sponding round-the-corner torque-versus-deflec- 
tion characteristic of the orthopentax linkage, 
through application of the axial torques above 
introduced. It may be shown that this process 
leads to stability in the semiconstrained gyro 
assembly, which in fact then has the properties 
of a lead-computing sight. The “time constant” 
of the kinematic computer thus formed depends 
on the moment of momentum of the rotor and 
on the applied torques, and might be made as 
long or short as desired. A number of advan- 
tages have been thought to be possible of reali- 
zation in this type of mechanism over the clas- 
sical types. The attractive possibility which sug- 
gests itself, of applying torques to the inner 


IQNFIDENTIAU 


78 


LINKAGES FOR COMPUTATION AND MANIPULATION 


gimbals of the orthopentax mounting through 
eddy-current drag between them and the rotor, 
is spoiled when it is recognized that negative 
time constants are thus obtained, although in- 
deed the motion is aperiodic. A reversal in ro- 
tation, between the rotor and whatever drag- 
disks were used, would be required. Such a 
procedure was entertained at one point in the 
PUSS development, and although shelved as a 
tangible plan was never wholly discarded. 

The writer has found that the orthopentax 
might serve in the construction of analog as- 
semblies for geometrical models in the synthesis 
of airplane flight. In such synthesis the com- 
plex relations among dive, pitch, turn, bear- 
ing, roll, and bank must be embodied precisely 
for complete effectiveness. Automatically, these 
relationships are displayed by the orthopentax. 
Suppose, as usual in such synthesis for flight 
simulation, we choose axes in the airplane, so 
that the framework of the linkage, as we have 
considered it above, is fixed with respect to the 
vehicle. Let one of the stationary axes be 
aligned with, and thus represent, the longi- 
tudinal axis of the airplane. Let the other sta- 
tionary axis of the linkage be parallel and thus 
represent the ‘‘line of the wings,” normal to 
the airplane’s axis of symmetry. This orients 
the linkage in the airplane completely. The axis 
of the gnomon should now be made coincident 
with, and consequently to represent, the true 
vertical. Under these conditions it will be ob- 


served, particularly if a model is constructed 
and manipulated, that dive and bank, which are 
angles with respect to the vertical and hori- 
zontal, are represented directly by rotations in- 
volved in, and measurable or manipulable in, the 
bearings between the terminal members and the 
inner members of the linkage. Further, roll and 
pitch of the airplane, which are generally consid- 
ered, but need not be, as indefinite integrals of roll 
rate and pitch rate, are embodied directly in the 
bearing rotation of the terminal links in the 
framework. Turn and bearing, somewhat differ- 
ently, are embodied by the geometry between the 
linkage as a whole and an external horizon-com- 
pass reference system. Since these quantities are 
mechanically available in the linkage, it was con- 
templated that such an assembly might be di- 
rectly installed in synthesizing structures, 
where it could carry out the “computations” 
inherent in its nature, as a substitute for more 
complex analytic assemblies of components. The 
exact character of the representations would 
there provide an attraction as well. The method 
was not employed, however, in the projects thus 
far completed, since in them certain somewhat 
more rudimentary approximations were felt to 
be adequate in the initial stages. It is considered 
that in future work, now being planned on such 
simulative projects, for airplanes and less ortho- 
dox vehicles, the orthopentax may actually be 
pressed into service as a comprehensive mechan- 
ical computer. 


Chapter 6 


AIMING OF TORPEDOES FROM AIRPLANES 


6 1 THE WEAPON ITSELF 

A S A SELF-STEERED projectile, of which class 
there are many contemporary airborne 
counterparts, the underwater torpedo'^ was 
early and famous. A rich literature describes 
its development and relates its illustrious his- 
tory. The aiming methods are well known, for 
launching both at and below the surface of the 
water. In United States Services, practically all 
torpedoes launched from airplanes have been 
of the so-called straight-run variety, which 
maintains the direction of the missile in effect 
at release, or when the gyro is uncaged. Sub- 
stantially all our experience in the preparation 
of sights and computing systems has been with 
this type, and specifically with early “mods” 
of the torpedo Mark 13. Militarily, the history 
of the tactical use of the torpedo in World War 
II is well known. Having made a bad start, 
with very heavy squadron losses in several en- 
gagements, somewhat of a renaissance was evi- 
dent in the use of the torpedo from airplanes 
during the last year of the war in the Pacific. 
Improved projectile stability may have been a 
heavily contributory element in this trend. The 
weapon itself, however, has unrivalled quali- 
ties against major fleet units. It is believed by 
many in our branch of activity that the employ- 
ment of a good computing sight might have 
made torpedoing from the air a much more at- 
tractive mode of warfare, not only in the exe- 
cution of operations but, in particular, to the 
warrior himself. The prejudice against torpedo 
sights, which has been evident among oper- 
ating personnel in general, may have had basis 
partly in the violence of the approach tactics 
which were felt necessary, and which allegedly 
disallowed the delicate matter of sighting, but 
it is now generally believed that this prejudice 
arose from experiences with the rather in- 
adequate sighting systems which were at first 
provided. 

“The term denotes self-propulsion as well, in its 
modern connotation; earlier usage preferred the auto- 
mobile torpedo. 


For the purposes of this report, the projec- 
tile may be considered to fall as a bomb in vacuo 
from the launching vehicle into the water, hold- 
ing a constant body heading, and thence to 
proceed, with respect to the water and sub- 
merged at a set depth, in a direction deter- 
mined by the above heading and consequently 
by the compass heading of the torpedo air- 
plane at the instant of release. Although at first 
the speeds and altitudes at which the torpedo 
might effectively be released were somewhat 
limited, these limits were considerably relaxed 
by subsequent developments. Entry angles in 
the vertical plane, governed by a relation be- 
tween altitude, speed, and glide angle at re- 
lease, were similarly made less critical. It is 
not our purpose, however, here to discuss such 
properties of the projectile, nor indeed are we 
qualified so to do. We merely record such back- 
ground as is supposed the minimum for a rapid 
grasp of the instrumental developments. 

The water speed Vt of the torpedo is fixed, 
and is known to within better than 10 per cent 
on the average. In the projection of a torpedo 
from any point in the air toward an immova- 
ble point a range R ahead, the average speed 
Vatf including both air and water travel, is 
valuable to know. This is evidently the ratio 
of this range to the total time consumed, or. 


Vat = 


R 


tf + 


R — V alf 


Vt 


1 - (Fa - F,) 


where also tf is the time of fall in air of the 
torpedo, and Va is the “ground” speed, or 
strictly speaking the water speed, of the air- 
plane. For horizontal flight this time is given 
substantially hy j^'2h/g, h being the airplane's 
altitude over the water. Consistent physical 
units are everywhere assumed to be used. 

It is seen that when the range is infinite, as 
it cannot be except mathematically since in 
particular the projectile runs out at 4,000 
yards or so, the average speed is merely the 
water speed. At the other extreme, when the 


CONFIDENTS 


79 


80 


AIMING OF TORPEDOES FROM AIRPLANES 


range is merely the speed of the airplane into 
the time of flight, it is seen that the average 
speed of the missile is simply the airplane 
speed. This reduces the torpedoing mission to 
one of bombing, which is inadvisable since an 
arming run in the water, normally some 200 
yards, is essential. Thus between the limits set 
by practical conditions no singularities exist 
and we may safely use the relation: 

1 . 

1 _ (y. _ y,) 

R 


6.2 BRIEF HISTORY OF OUR 

DEVELOPMENTS 

Beginning in the earliest days of the air- 
borne Are control contract (OEMsr-330) at The 
Franklin Institute, Section 7.2 of Division 7 was 
associated with the development of a series of 
computing sights for airborne torpedoes. In the 
Services this work began under Navy auspices 
entirely, with Project NO-106 for the design 
of such sights, but in later efforts it became 
partly recognized under Army projects as well.'’ 

Torpedo directors'" of the commonest general 
type involve an estimate of the target’s speed 
and relative course, to be made by the pilot 
before the attack is begun. We shall refer only 
to those in which the relative course setting, 
once made, is automatically corrected for turn- 
ing of the airplane, or in which the compass 
course of the target is, as we may say, 
stabilized in the director. The manner in which 
it has been preferred to set in the target course 
is through manual alignment, of a body in the 
airplane representing the target, into a posi- 
tion parallel to the heading of the target itself. 
Certain unstabilized directors, notably torpedo 

*’In most of the work on these projects undertaken 
since 1943, A. L. Ruiz has been the responsible over- 
seer rather than the present writer. (See Part II of 
this volume.) 

'A computing sight for torpedoes, typically a lead 
computer in the most literal sense of the term, has 
traditionally come to be called a director. Special 
types of aiming controls for torpedoes, to be de- 
scribed later, more nearly merit such terminology; 
but in spite of the illogical nature of the term in the 
present connection we shall use it here in an effort 
to conform. 


directors Mark 28 and Mark 30, were in 
production prior to our activities, and are men- 
tioned here only by way of comparison, al- 
though one of the projects latterly undertaken 
was the provision of automatic target-course 
stabilization for the torpedo director Mark 30. 

All the computers involved in the directors 
which were developed under this project were 
of the vector type, involving the target veloc- 
ity vector, presumably set in magnitude and 
direction by reconnaissance, a potential torpedo 
speed vector along the airplane’s heading and 
consequently Axed in direction in the vehicle, 
and a computed unit vector to be directed 
toward the target by appropriate maneuvers 
in fulfllling the aiming criterion. 

Early efforts dealt with the construction of 
mechanical models involving manual settings of 
target speed and course, airspeed and altitude 
of the airplane, and the torpedo run, for which 
the range to the target at the time of release, 
the so-called present range, was taken as a 
sufficiently valid approximation. Stabilization 
of the target-velocity vector was accomplished 
by servo-repeater from a directional gyro. The 
output of the computer rotated a reflecting sight 
bodily, about a vertical axis in the airplane, 
establishing the line of sight to be directed at 
the target. 

An analogous director was also constructed 
experimentally using electric computation, with 
alternating currents representing vectors in 
amplitude and phase. Electrical servos were em- 
ployed for introduction of airplane course from 
the directional gyro, and for manipulation in 
azimuth of the pilot’s sight head. Such experi- 
mental systems were installed in a mock-up in 
the laboratory in order to assess their possible 
effectiveness in terms of the occupation of space 
and of the ease with which operations might 
be made on them in practice. The principal task 
appeared to be that of reducing the size and 
weight, and this was made clear by the military 
personnel who were consulted and to whom 
proposed forms of the apparatus were demon- 
strated. 

As an attempt markedly to reduce size and 
weight, a miniature director was then conceived 
and designed, which was entirely mechanical 
and which occupied only a 4-inch cube in the 


BRIEF HISTORY OF OUR DEVELOPMENTS 


81 


airplane. This director derived target-course 
stabilization directly from the directional gyro, 
on which it was physically superposed. For- 
tunately this was possible since that flight in- 
strument was normally placed at the top and 
in the center of the instrument panel, so that by 
cutting an opening in the horizontal cowling a 
mechanical connection could be made from the 
director, placed directly between the windscreen 
and the head of the pilot, via an adaptor on the 
directional gyro to the outer gimbal of that 
instrument. A clutching arrangement was pro- 
vided so that the operator might quickly con- 
nect or disconnect the stabilizing link between 
gyro and director, thus making it possible to 
remove from the directional gyro even the 
minuscule load imposed by the stabilization on 
that flight instrument when the director was 
not in use. The pilot set into the director the 
several variables mentioned above by the manip- 
ulation of a set of small dials which faced him. 
A stationary post and a movable bead estab- 
lished the variable line of sight in azimuth, 
which, by maneuvering the airplane, the pilot 
was to align on the target as an aiming cri- 
terion. All computation was by a condensed 
system of cams and links. 

After several experimental models were con- 
structed of this instrument, of which the final 
units were tested by the Navy, it was placed in 
production as the torpedo director Mark 32^ 
and became standard equipment on some tor- 
pedo airplanes. 

Several modifications of the torpedo director 
Mark 32 were experimentally pursued under 
Section 7.2 projects. Versions were worked out 
for Army employment, wherein somewhat dif- 
ferent operating requirements had to be met. 
It was necessary, for example, to alter the cali- 
brations in terms of which the input variables 
appeared, this being admittedly a rather trivial 
development. In one case, however, the comput- 
ing mechanism of the Mark 32 was adapted to 
remote indication of the lead to the pilot, in- 
volving both mechanical and electrical repeater 
components, and with special arrangements for 
stabilization from existing army equipment and 
means conveniently to establish the estimated 
target course. This latter operation, wherein the 
pilot must be enabled to adjust manually an 


index of some sort into a direction analogous 
to that of the target ship, came in for consider- 
able research effort in all the torpedo projects 
we dealt with. The problems of foolproof clutch- 
ing, to satisfy both the requirements of light- 
ness and speed in declutching, and also to retain 
sufficient strength to avoid breakage when 
wrongly manipulated, were not insignificant. 
It was desired to permit this input setting to 
be made by the pilot, with one hand and with- 
out needing to see the adjustment he is mak- 
ing, that is while keeping his eyes on the target. 
Numerous experiments were thus made with 
stylized ship models which could be grasped in 
the hand and turned about a vertical axis in the 
airplane, and which would immediately and 
uniquely impart, by touch alone, their orienta- 
tion in comparison to a visual reference. 

Projects which required less original devel- 
opment, but which were undertaken in view of 
specialized experience which had been gained, 
included those for applying target-course sta- 
bilization to other torpedo directors. One such 
project involved the torpedo director Mark 30. 
As source of stabilization the reference was 
generally the directional gyro, adapted some- 
what as before for the Mark 32, but now with 
the attachment of followers such as the Telegon 
and the Magnesyn connected through a variety 
of experimental servo channels. These stabiliza- 
tion projects usually appeared in combination 
with the setting of target course, since the 
stabilizing action usually added to that input, 
once made. 

Stabilization was also provided for a motor 
torpedo boat director of existing design. This 
director itself was of simple vector type and 
was used visually. The target course was incor- 
porated by a mechanical part therein, and was 
stabilized by appropriate connections with the 
flux gate compass circuit on the vessel. Follow- 
ing tests in which the equipment was found to 
function as desired, the whole outfit was deliv- 
ered to BuShips. In the course of this work, 
which constituted rather a digression from air- 
borne activities, several suggestions were sub- 
mitted for alternative modes of operation, to 
remedy certain defects in the sequence of opera- 
tions, but these need not be described in detail 
since they lead to methods precisely analogous 




82 


AIMING OF TORPEDOES FROM AIRPLANES 


to those proposed for airborne versions. Such 
proposals are described in Section 6.5. Further 
on torpedo boat applications, a certain amount 
of consultation on aiming controls was provided 
to other groups who were concerned with the 
“blind’' attack problem, employing the SO 
search radar, for example. 

In response to a Navy request, a modification 
of the torpedo director Mark 32 was worked 
out which permitted manual stabilization for 
applications in which this director was intended 
for standby operation in patrol airplanes, and 
in which automatic stabilization was not con- 
sidered feasible. The attraction here was merely 
compactness of the computer and the presenta- 
tion, and the extended development involved 
only the design of an inverted mounting and 
certain recalibrations. 

Although no equipment of such type has been 
constructed, much thought and certain theo- 
retical work has been done on what were called 
two-man directors for torpedoes. The general 
scheme of these differs radically, with regard 
to the sequence of operations, from the standard 
forms, although in fact the aiming principles, 
or the equations solved, are identical. Whereas 
in the regular director the airspeed vector, and 
hence the torpedo speed vector are inherently 
incorporated through the fixed orientation of 
the vector computer in the vehicle, in the two- 
man version the direction of this vector is the 
output of the system and provides an index 
of heading to which the pilot maneuvers the 
airplane. Further, instead of so flying that the 
generated line of sight, which is the output of 
the standard director, points at the target, in 
the two-man version one operator tracks the 
target and supplies that direction as an input. 
Several advantages obtain under this method 
of operation, simplification of the pilot’s task 
being the principal one. As already pointed out 
no such directors have been built for airborne 
use, although possibly this might be of interest 
for the future, particularly where the newer 
torpedo bombers contemplate pilot and copilot, 
sitting close together and side by side. For the 
PT boat director, however, an experimental 
adaptation was made in the laboratory for such 
two-man operation. In the actual operation the 
helmsman was to steer to a compass course 


automatically established on his panel, or keep 
an indicator of course error on or near zero. 

In the earlier directors the run of the torpedo 
was estimated in terms of the range to the 
target. For relevant cases these variables differ 
significantly. Thus it was desired, since also 
the “present range” was latterly available from 
ARO radar, to develop a director in which this 
variable, rather than the torpedo run, would 
be accepted directly by the computer. It had 
been evident earlier that the transformation, 
from range to run, could be made instrumen- 
tally by a mechanical process of successive ap- 
proximations. No adequately simple such mech- 
anism was arrived at. Somewhat later it was 
pointed out by the present writer, however, that 
a simple linkage existed which accomplished 
this transformation implicitly. On the basis of 
this linkage, and of the several variants which 
it allowed, a series of so-called present range 
directors were constructed, under Army and 
Navy projects. For descriptions of these direc- 
tors, see Part II. A brief exposition of the fun- 
damental geometry involved in the computing 
linkage is given in a subsequent section of the 
present report. 

The vector computer in its simplest form is 
based on the somewhat dangerous assumption 
that the target course and the target speed are 
unchanging quantities from the moment of 
their estimation until the torpedo gets to its 
mark. In general this is not the case, and con- 
sequently significant error may result from 
such an assumption. Failure of the course and 
speed of the target, evaluated at a given instant, 
to predict the subsequent track thereof in space 
and time is due to accelerations which are pres- 
ent in the intervening regime. These may begin 
during the attack, in the form of incipient eva- 
sion, or may have been in process in expecta- 
tion of attack. The smallness of available acceler- 
ation and the delay in initiating it, from the 
enemy point of view, makes the latter type of 
evasion preferable in typical cases. In any case 
a serious problem in counterevasion measures 
is presented. Early features of torpedo direc- 
tors, intended for outsmarting the prospective 
evader of torpedoes, included such simple means 
as an optional modification of the target-speed 
vector, imposed under choice of the pilot on 


THE ELEMENTARY VECTORIAL SOLUTION 


83 


observation of existing or impending evasive 
tactics. Such modification, for application in 
average circumstances, consisted, for example, 
in a 15 per cent reduction in target speed, as 
set into the computer, coupled with a 10-degree 
rotation of the target course applied in the 
appropriate sense. An extensive program 
of study leading toward a more articulate 
counterevasion development program was un- 
dertaken in cooperation between our contractor 
at The Franklin Institute and the Statistical 
Reseai’ch Group under AMP at Columbia. These 
studies included theoretical investigations, 
based on available knowledge of the capabilities 
of enemy targets, and have been embodied lat- 
terly in a program for the design of a computer 
which would incorporate an optimum handling 
of the evasive situation for practical purposes. 
(See Part II.) 


the elementary vectorial 

SOLUTION 

The problem*^ of so projecting a torpedo as to 
hit a stationary target is one largely of putting 
the torpedo into the water and of directing it 
straight at the target. From the moment of 
release until the trip is ended the course thus 
set will be maintained by the directional con- 
trols of the torpedo itself. The distance of the 
target from the point of release — its range, 
that is, — need not be accounted for if it is 
within the maximum range of the torpedo ; and 
neither does the torpedo’s own speed. For the 
conventional torpedo these observations apply 
equally well when the target has a real velocity 
but is either receding or advancing on a straight 
line from the observer, although of course the 
presentation of the target may not be the most 
desirable under such conditions. 

In directing a torpedo at a moving target it 
is hoped that the motion of the target will 
continue unchanged, at least during the run of 
the torpedo. If the travel time of the projectile 
were very short, as with a ray of light or other 
radiation, this hope would be nearly fulfilled. 

'‘Some of the text of the present section, and also 
of the remaining sections of this chapter, has been 
adapted from earlier informal reports and notes of 
the writer; such reports have not otherwise had wide 
distribution. 


Since the speed of a torpedo is one of the order 
of that of the target, however, its travel time 
is not inappreciable but is an important con- 
sideration, especially if the motion of the tar- 
get is of the more general sort. 

In general a prospective target, say a ship, 
will be headed on a course which lies at an angle 
cz to the line of sight from an observer, and will 
have a certain speed or velocity Vs on that 
course. Its motion may thus be described by a 
vector having this speed for magnitude and di- 
rected in the above manner. From the same 
observation point a torpedo is to be projected 
in such a way as to meet the ship if the latter 
continues on its present course at its present 
speed. The torpedo has a known speed Vt in the 
water (we assume pro tern that the torpedo 
makes the entire trip in the water; air travel 
corrections are elsewhere considered) , and may 
be directed at some angle ^ to one side of the 
line of sight. There is thus formed a “torpedo 
speed vector.” Assume for the present that the 
torpedo enters the water and attains its speed 
immediately upon release. Knowing the torpedo 
speed Vt and having estimated the ship speed 
Vs and course angle a, the problem is to obtain 
and employ the appropriate directing angle 
the “lead” angle for the torpedo. (A better sym- 
bol would be A, but again we should run counter 
to one established convention in trying to fol- 
low another.) 

Assumed successful, the travel time of the 
torpedo, subsequent to the moment of release, 
will be the same as that of the target. The dis- 
tances traveled, then, by ship and torpedo 
respectively, will be VsT and F^T, T being the 
travel time, and will form two of the sides of 
a triangle as shown in Figure 1. The angle a, 
and if properly chosen the angle will be 
angles of the triangle as shown. These relations 
suffice to give fS in terms of the other quanti- 
ties, for by application of the law of sines 


VsT 

VtT'' 


and hence 
where 


Vs sin i8 
Vt sin a 


sin /3 = 12' sin a, 


12 ' = — 




( 2 ) 


(3) 


If the target is stationary. Vs vanishes and 


84 


AIMING OF TORPEDOES FROM AIRPLANES 


SO also does When the target is moving on 
the line of sight, as considered before, then a 
is either zero or 180 degrees and again /? is 
zero. Otherwise /? will have a nonzero value 



and will in any case show the proper direction 
for projection of the torpedo. 

In this solution of the directing problem, it 
will be noted that the range itself does not 
enter. Thus in Figure 1, where for a particular 
case the appropriate torpedo vectors are shown 
at a variety of surrounding points, these vec- 
tors are shown to be unchanging along radial 
lines from the target. Furthermore the speed 
of the vehicle is assumed here to be ineffective, 
the torpedo rapidly assuming a velocity of its 
ovm after being released. All information is 
thus contained in the lead angle Since with 
conventional methods the torpedo’s direction 
upon and following release is that of the longi- 
tudinal axis of the airplane, and not the di- 
rection of the flight path, it is only necessary 
that this axis be directed at the angle p from 


the line of sight. In the torpedo director this 
is arranged for by automatically turning a 
sight in the opposite direction through the 
same angle ^ with respect to the thrust axis of 
the plane. When the target is in the sight the 
plane is properly directed. If it is kept in the 
sight release may occur at any chosen instant. 

In general the desired lead angle which is 
also the sighting angle, in the opposite sense, 
will not be constant but will vary as the plane 
comes in on a course such as that shown in 
Figure 1. The existence of such a course pre- 
supposes that the airplane’s axis coincides with 
the instantaneous direction of its flight path, 
and is one of a number of possible courses ob- 
tainable by following the torpedo speed vec- 
tors of the figure. This is with the assumption 
of no sideslip. If there is sideslip the accuracy 
of aiming is not affected but a different sort of 
course will be followed. For example the plane 
may be flown on a path directly toward the 
target, if it is continuously sideslipped so that 
the target always appears in the sight. Under 
this condition the lead angle (i will be almost 
perfectly constant, since the plane speed itself 
is relatively so great. 

The torpedo director in the airplane, which 
gives the lead angle fi by rotation of the sight, 
must do so through a continuous knowledge of 
the quantities a, Fg, and Vt. The latter is known 
in advance, being a property of the torpedo. 
The two former may be accounted for, assum- 
ing the target will continue on an existing or 
predictable course and speed, by means of a 
ship speed vector involved in the director mech- 
anism. Having once been set, as by preliminary 
observation, the magnitude and direction in 
space of this vector are not allowed to vary. 
Thus the direction must be stabilized, as with 
a directional gyro. This ship speed vector, in 
combination with the torpedo speed vector, the 
direction of which is merely that of the plane 
axis, gives the sighting angle automatically. 
Figure 2 shows three equivalent graphical so- 
lutions, set up as though at the point B of 
Figure 1. In Figures 2 A and 2B the direction 
of sight is shown as the direction of the vec- 
tor difference between the torpedo speed vec- 
tor and the (stabilized) ship speed vector. In 
Figure 2C the sight direction is that of the 


RESULTS OF ERRORS IN TARGET MOTION 


85 


sum of the torpedo speed vector with the nega- 
tive of the ship speed vector. 

Naturally there are a number of ways in 
which this solution may be carried out physi- 



Figure 2. Relations at point B of previous figure. 


cally. One important problem is to provide for 
errors which may occur if the plane banks, for 
it is inconvenient to stabilize the whole director 
mechanism in space. Optical arrangements are 
possible so that the target always appears dead 
ahead in a stationary sight. For example one 
of a pair of mirrors may be rotated through 
an angle ^/2. Such proposals, however, have 
hitherto been unpopular. 

It will be noted that it is not absolutely nec- 
essary to adjust for both F« and Vt, since only 
their ratio o' is ultimately involved. It might 
be thought mechanically simpler to adjust Vt 
only, so to speak, leaving Vg fixed at some ref- 
erence length, but this would give an infinite 
length on the Vt scale when Vg were zero, as 
for a stationary target. 

One may notice, either geometrically or from 
equation (2), that when O' > 1 two solutions 


for p may result. Both produce hits, although 
that for the longer torpedo run is ruled out by 
a mechanical computer. Other troubles arise 
in the region about O' = 1, but fortunately the 
lower values are predominant in practice. 

6 ^ RESULTS OF ERRORS IN TARGET 
MOTION 

It is necessary, since this type of director is 
based on visual estimation of course and speed 
of the target, to consider the effect of errors 
made in estimating these properties or in set- 
ting them into the director. This study will not 
completely apply to such errors when due to 
changes in the properties of the target since 
last observed, or which are due to such causes 
as imperfect directional stabilization, over a 
period of time, within the director itself. 

In Figure 3 the general case is shown, where 
Vs is an erroneous setting of the exact target 
speed vector V^. In this case both target course 
and target speed are assumed to be in error. 
As a result, even though the target is perfectly 
sighted, the torpedo is incorrectly directed 
along the supposed torpedo speed vector V', 
which differs in course by (radians) from 
the appropriate such vector V^. The same anal- 
ysis will apply for the corrected torpedo speed 
Nat- If the range for the torpedo, or the so- 
called run, is R as shown, the torpedo would 
miss a point target having constant speed and 
course by the amount, approximately 


M = . (4) 



Figure 3. Error in estimate of target motion. 


CONFIDENT-IABl 


86 


AIMING OF TORPEDOES FROM AIRPLANES 


The whole problem will be split into two 
parts; (1) the effect of errors in setting target 
speed only and (2) the effect of errors in target 
course only. Figures 4 and 5 are drawn for 
these two cases respectively. 



Figure 4. Error in estimate of target speed. 


V' 

s 


The fractional error in setting the length of 
may be called v 


K- V. 


( 5 ) 


where the speeds V\ and are merely the 
scalar magnitudes of V' and ¥«. 



Figure 5. Error in estimate of target course. 
We find, to a good approximation, 




Q,' sin a 

— 

4/ 1 — sin2 Q, 


(6) 


This gives the error in torpedo course due to a 
fractional error in the target speed setting. Let 
us obtain the corresponding value of Aj 3 for 
an angular error fx in the target course setting. 
Referring to Figure 5 , then. 


H — oil — q;, (7) 

We find, corresponding to equation (6), 




cos a 

4/1 — sin^ a 


( 8 ) 


Equations (6) and (8) show errors in torpedo 
directing due to the fractional errors v and 
as functions also of n' and a. The amount of 
the resulting miss depends on the torpedo range 
as given by equation ( 4 ), or by 



Since a convenient dimensionless form for the 
miss is M/Rof Ro being present range, we may 
write 


M R , 

~ Ro~ Ro^^’ 


( 9 ) 


and consider and as the errors, expressed 
as fractions of present range, due to the ini- 
tially committed fractional errors v and fx 
respectively. Thus 


R 12' sin a 

w / - = "■ 

sin'i a 


R fi' cos a 

(f, = fi. 

siii2 a 

Now since 

R sin (a + /8) = Rq sin a, 
we have finally : 
ev 12' sin a 

^ 1 — fi'^sin^a + 12' coso: 4 / 1 — fi'^sin^a 


( 11 ) 


( 12 ) 




- ( 13 ) 

1 — 12'2 sin^ a-\- 12' cos o: 4 / 1 — 12'^ sin^ a 


The functions ejv and of 12' and a, may 
be considered as error-transfer factors which 
show how the errors in setting target proper- 
ties carry over to a miss on a point target. 

By means of the relations 


and 


sin jS = 12' sin a, 


sin 7 = sin (q! + ( 3 ). 

The factors in equations (12) and ( 13 ) may 
also be expressed as functions of o' and or 
of o' and y, and so on. Results of computation 
may be graphed or tabulated against these 
variables for convenience in inspection. 


^NFIDTINTlAir 


TWO-MAN OPERATED DIRECTORS 


87 


In connection with errors such as those dis- 
cussed above, especially if the results are to be 
used to show favorable types of approach, there 
is an important modification which arises from 
the varying width of a given target as seen by 
the torpedo. The effective “diameter” of the 
usual target, from the torpedo point of view, 
varies with the angle y between the target and 
torpedo courses, and changes from a minimum 
when y = 0 degrees or 180 degrees to a maxi- 
mum when y = 90 degrees. It is the particular 
shape of the target which 'determines the varia- 
tion of this diameter for intermediate values 
of y. 

If an ellipse is taken as resembling suffi- 
ciently closely, say a battleship, then it may be 
shown (Figure 6) that the ratio of effective 
diameter to the length is given by 

— 7 } cos^ y. 

An average eccentricity rj, for warships, is 
about 0.988. 



Figure 6. Intermediate diameter of ellipse. 


6 5 TWO-MAN OPERATED DIRECTORS 

With the pilot-operated director described, 
the principle of which is illustrated for exam- 
ple in Figure 7, the airplane heading is so 
varied that an automatically computed vector 
lies along a line of sight to be aligned with the 

AIRPLANE 
COURSE 

f 



target. This vector is merely the difference be- 
tween a unit vector directed as the airplane 
(and hence as the torpedo) and another vector 
directed (and stabilized) as the target and of 
length equal to the ratio o of target speed Vs 
to average torpedo speed Vat in air and water. 

The latter vector is manually set after esti- 
mation of the corresponding properties of the 
target motion. 

Since direction only of the computed sight 
vector is important, this vector may be re- 
placed by a unit “range” vector Ro/Ro as shown, 
making the angle j3 with the airplane heading. 

If, for convenience, the symbol is used for 
a unit vector, then Ro/Ro niay be denoted by 


LINE OF 
SIGHT 


\ 


SBnSdEntiaL 9 

— ^ I 


88 


AIMING OF TORPEDOES FROM AIRPLANES 


iPr. Similarly Yat/Vat ^Yt/Vt may be repre- 
sented by the symbol if/t, and Ys/Vs by xj/s. The 
simplified vector picture is shown in Figure 8. 
Mathematically, 

kxpr = 

k and O being scalar quantities. (In fact, k 
is the ratio Rq/R of target range to torpedo 
run.) 



Figure 8. Expression of classical solution in unit vectors. 

The angle between the sighting line (deter- 
mined by xf/r) and the airplane or torpedo di- 
rection (determined by xj/t) is the angle /3 by 
which the target must be “led’' to secure a hit. 
It is not constant but varies during any ap- 
proach of general sort. It may be noted that 
there are two “sight lines,” and hence two dif- 
ferent angles which might be called /?. One is 
the actual line of sight to the target and the 
other is a line in the direction of the pilot’s 
physical sight in the rotation of which the di- 
rector results. If it is considered that the sym- 
bol ^ describes the latter, the former may be 
called The pilot’s efforts during attack are 
directed toward making ^ which is his 

release condition. It is important to notice that 
varies while the airplane is being operated 
in an attempt to make good this equality. 

It has been proposed that a director might be 
considered, operating on the same principles as 
this one, but in which the work of keeping a sight 
on the target and of directing the airplane is 


divided between two individuals. The pilot-op- 
erated director assigns these duties to one man. 
This, it should be explained, is one of its merits, 
in that it is possible thus for a single operator 
to perform these functions. A two-man director 
would merely be used to simplify the pilot’s 
routine and also to relieve the stringent space 
restrictions around the cockpit. In the bombing 
airplanes, for example, the director mechanism 
might be located at the bomber’s station, com- 
municating with the pilot only through the me- 
dium of a pilot’s direction indicator [PDI]. It 
is interesting to note that in such a director it 
would be possible to employ the same mechan- 
ical computer and stabilizer as was developed 
for the pilot-operated version. 



Application of the director principle already 
described to a two-man instrument might be 
made as shown in Figure 9. With the unit tor- 
pedo (or airplane) vector xf/t still fixed in the 



TWO-MAN OPERATED DIRECTORS 


89 


airplane, and the relative target speed vector 
Qij/s set in as usual, the unit range vector xpr 
along the resultant shows where the target 
should appear if a solution is to be obtained. If 
the actual direction of the target is tracked 



manually, as determined by another unit range 
vector the real unit range vector that is, 
then the angle K between if/r and if// gives a 
measure of how far the computed sight line is 
from the actual sight line. This error angle 8r, 
which might also be called A/3, as is evident 
from Figure 9, is an indication likewise of which 
way the airplane should be turned, though not 
truly how much, to bring about a solution. That 
is to say, if 8r = = 0, then the airplane is 

properly directed. If the winding and contact, 
respectively, of a potentiometer are attached to 
the unit vectors if// and if/r, the deflection of a 
meter on the pilot's instrument panel can show 
him how to direct his airplane. 

The mechanism shown in Figure 9 requires 


three slip rings and a potentiometer winding to 
be attached to the director mechanism, as well 
as a downward periscope directed along if/r, re- 
placing the pilot’s sight. Rotation of the peri- 
scopic sight and of the stabilized target vector 
(^if/s) takes place about flxed points: the ter- 
minals of the unit torpedo vector if/t. 

If it were allowable either for the stabilized 
target vector or for the sighting arm to rotate 
about a point not perfectly stationary in the 
airplane, then two alternative forms of two-man 
director immediately become possible. These 
are built around the same basic mechanism con- 
sidered above, but differ from the director 
schematically shown in Figure 9 in two respects. 
First: only one slip ring is required, since the 
potentiometer winding can be stationary. Sec- 
ond: the indication given the pilot may be al- 
ways directly proportional to the amount 8r by 



which he is away from the desired course. In 
these two variants, which are shown in Figures 
10 and 11, the whole director mechanism rotates 
as the target is tracked. 

Returning to Figure 9, here the operator 
tracks the target directly with if//, having set 


90 


AIMING OF TORPEDOES FROM AIRPLANES 


in target speed and course which are absorbed 
in the henceforth stabilized vector Ci\f/s. Since 
the unit resultant vector xf/r will in general not 
lie along xf/r\ as it should for a solution, there is 
an angle, having a definite sense or polarity, 
between xj/r and xf//. This angle unbalances the 
bridge circuit shown and thus indicates to the 
pilot the direction, and in some measure the 
degree, in which the airplane must be turned. 
If, however, the airplane is turned merely 
through the angle S,., a residual indication will 
remain, since xps and xj/t do not maintain a con- 
stant relationship during a turn of the air- 
plane. This should not necessarily prevent 
reduction of Sr to zero, but it does indicate ac- 
tion in a closed loop, where stability questions 
may always arise. 

Operation of the two mechanisms of Figures 
10 and 11 may be described together. Here 
the whole vector triangle is rotated about one 
end or the other of the vector xf// in such a way 
that xp/ tracks the target. The target speed- 
and-course vector has already been so set 
that xpt shows the proper heading for the 
airplane. The actual heading being given by 
the stationary vector xj/t, the angle St between 
xpt and xf// is the true angle through which 
the airplane should be turned. To indicate 
this angle continuously to the pilot, a poten- 
tiometer with stationary winding and a con- 
tact point driven by xp/j as shown, will suffice. 

Since the only continued manipulation re- 
quired of the operator is that of tracking the 
target, he would probably find time to keep 
well up to date the settings of target .speed 
and course. Release of the torpedo, say by 
the pilot, could be made when he and his 
“confederate” were both satisfied, as indicated 
by appropriate signals or interphone discus- 
sion, with the general prospects of a hit. 


6 PROBLEMS OF THE CONVERSION OF 
PRESENT RANGE AS INPUT 

In the torpedo director the ratio 



between ship speed and torpedo water speed 


must for precision be replaced by the corrected 
ratio 



between ship speed and an average torpedo 
speed applying to the combined air and water 
trip of the torpedo. Transformation from O' to O 
may be made reasonably well according to the 
formula 

x/h(V.-Vd 

O' 7.12 R 


where h is the altitude in feet at release, V„ 
is the component in knots of the plane's ground 
speed in the direction of the plane’s heading, 
Vt is the torpedo water speed in knots, and R 
is the torpedo run in yards. 

From the standpoint of the mechanism in- 
volving these quantities, it is convenient to 
consider 


Fa. 



ri5) 


as a sort of corrected ship speed, so that 


0 ^ ^ 

O' Vat Vs * 


(16) 


Thus a mechanical lever length in the director 
corresponding to Vt may be left fixed, and the 
air travel correction applied to another lever 
length representing F^, which is hereby changed 
to a length F^^ in the ratio given, say, by equa- 
tion (14). Still further, the length of the Vt 
arm may be fixed and defined as unity and 
length of the Vs arm set at o' (or at o for the 
corrected case) on the numerical scale thus 
defined. 

In practice a dial is calibrated in Vg itself 
and the correction given by equation (14) is 
included automatically; h, Va, and R being set 
in normally on other dials. 

The altitude may be difficult to obtain with 
any precision, unless special instrumentation 
is available. Fa, it will be noted, is not the air- 
speed itself unless no wind is experienced, so 
that a precise setting here may depend on 
knowledge of speed and direction of the wind. 
However, if these quantities are at all exactly 
obtainable it may be worth while to consider 
how the estimation of torpedo run R may be 




fcSNFIDENTIAL 


PROBLEMS OF THE CONVERSION OF PRESENT RANGE AS INPUT 


91 


improved. Substitution of present range Ro 
for R can be in considerable error. It has been 
said that R may be estimated as exactly as may 
Roy but this means only that the usual estimates 
of Ro are poor. If it is possible, by auxiliary 
means, to determine Ro closely, it will be ap- 
propriate to consider how conversion from Ro 
to R may be made without losing this precision. 
This is probably only advantageous if also 
reasonably close determination of h and Va are 
also possible. 

The director mechanism possesses a variable 
dimension which corresponds in magnitude to 
that of the second term on the right-hand side 
of equation (14), which may equally well be 
written 


where 


4/h (K - V.) 

” 7.12 /?o 


P 


Rq 

~r' 


Suppose, then, that with some angle a in 
effect, the speed ratio n and the angles /? and 
7 have been determined on the basis of an air 
travel correction which substituted present 



Figure 12. Embodiment of range-to-sun ratio. 


If this dimension is set on the assumption that 
P = ly or in other words if present range Ro 
is substituted for torpedo run R in the correc- 
tion adjustment, and if then this dimension be 
altered in the ratio p, the result will be the 
same as though the run R had originally been 
employed. It remains only to determine and 
employ the ratio p. 

If the air travel correction for torpedo speed 
be temporarily neglected, a value for p may be 
obtained which depends on any pair of the 
quantities: a, /?, 7 , fi'. Such a value would not 
be far from the precise value, which latter 
could not be explicitly obtained, by the arrange- 
ment described above, because a knowledge of 
P itself is needed for the correct determination 
of p (cf. Section 6 . 8 ). 

A more nearly precise value for p would re- 
sult when the air speed correction were made 
by substituting Ro for Ry and this is presum- 
ably the way the mechanism might work. A 
series of operations would occur within the 
director, each operation leading to a more ex- 
act value for p. It is evident that a closed causal 
loop is involved, as in a normal regulatory cir- 
cuit. The success and effectiveness of its opera- 
tion depends on how rapidly convergence takes 
place, if it does. 


range R^ for torpedo run R. It is evident from 
Figure 12 that the vector difference 


V., - V. 

has a magnitude equal to 


Rq Vat 

R 

In the normalized form then, as shown by the 
inset in this figure, where the vector Nat is 
replaced by the unit vector \ at/ Vat and where 
Vs is replaced by oVs/Fs, the corresponding 
vector difference 



has a magnitude which is simply 


(17) 


Rq 

R^ 

Thus in the director mechanism as planned 
there is a mechanical distance which may be 
calibrated directly in the ratio p. It is merely 
the distance, along the sighting direction, be- 
tween the pivot points corresponding to the 
two velocity vectors involved. In other words 
it is the length of the vector given by equa- 
tion (17). 


^ pONFIDENTMlT^ 


92 


AIMING OF TORPEDOES FROM AIRPLANES 


It is actually possible to accomplish this cor- 
rection explicitly, without the successive ap- 
proximation involved in the above method. See, 
however, the simpler solution given below. By 
the above relations, we have 


where 

^ A ( - F,) 

The factor $ involves only known and explicitly 
determinable quantities. 

From Figure 12 we have 

Rq sin 7 sin (a + « 

? D * * ^ 

K sin a sin a 

and of course 

sin (a + j 8 ) = sin a cos ^ + cos a sin 
The director is based on the exact relation 
sin sin a. 

Thus 

p = 4/ 1 — 12^ sin^ a + 12 cos at 
and consequently, 

“ = 1 — ^ 4 / 1 — 12 ^ sin^ Q! — 12 ^ cos a. 

This leads to the following quadratic equation 
in 12 : 

/ 1 , ^ ^ cos a \ /I \ 

+ 1 - r = 0. 

* ’ THE “COMPLETE SOLUTION” 

All previous solutions have been based on 
certain simplifying assumptions. The necessity 
for evaluation of certain instrumental and tac- 
tical approximations creates the need for a 
closed and explicit solution, without these as- 
sumptions, against which proposed approxima- 
tions could be tested in a precise and quantita- 
tive manner. No difficulties were encountered 
in obtaining such a solution, although mechani- 
zation on the basis of this solution was not 
primarily intended. 


Only in a relative sense is the term complete 
applicable to the solution given here. It should 
be understood that the following assumptions 
are retained. 

1. The target continues on a straight and 
unaccelerated path during the entire attack. 

2. The torpedo water course parallels the 
aircraft heading at release, terminal water 
speed and direction being attained immediately 
upon entry. 

3. The aircraft is in level flight at the in- 
stant of release. 

4. Aerial ballistic effects produce no distor- 
tion from a vacuum trajectory for the torpedo. 

5. The heading or thrust-direction of the 
aircraft defines the instantaneous direction of 
its path in the air. 

It is unimportant, for the type of director 
concerned (see Figure 13), whether a or 7 



Figure 13. Space diagram for straight-run torpedoing. 


is considered as the primary known target an- 
gle. Each is uniquely determined when target 
aspect is estimated and set, and each is auto- 
matically readjusted by the stabilizing agent. 
Both cannot be assumed known, since jointly 




NFIDENTIAL 


THE “COMPLETE SOLUTION’ 


93 


they determine which is the principal un- 
known. Solution for ^ may be expressed in 
terms either of a or of y, and in this case the 
latter will be taken. The run R is an unknown, 
but is here assumed to be computed inherently 
in the process resulting in a true value for 
The initial range Rq is assumed known. Wind 
velocity, airspeed, torpedo water speed, and 
target speed, or Va, Vt, and Vs, are all as- 
sumed to be known, as is also the wind bearing 
6 with respect to aircraft heading. 

In connection with 6, it should be pointed 
out that this is the angle between the aircraft 
heading and the positive direction of the wind. 
The supplement of 6 gives the angle from head- 
ing to the direction of the wind source, to which 
reference is usually made in denoting the com- 
pass bearing of wind. It will be noted from the 
figure that the angle between target heading 
and the compass bearing of the wind is simply 

From assumptions 3 and 4 we may relate al- 
titude h and time of flight tf by the formula 


to the aircraft heading, or the torpedo water 
run. Thus 

Ro sirijS = TVs sin y — t/Vy, sin d, (22) 


Ro cosiS = TFsCos y tfVy, cos d 

-hTVt + tfiVa-Vt). ( 23 ) 


Now using the abbreviations, and appropriate 
physical units. 


^0 


i/H{V„-V,) 

iRo 

V. 


( 24 ) 

( 25 ) 


= 


tan /3o = 


Vw 

(Fa - V7)’ 

^8 sin y 
1 + 12s cos y ’ 


( 26 ) 

( 27 ) 


«o( 


, , ^ sm (7 + 0) , sin 

I “r . — “r . 

Sin y 12s sin 




( 28 ) 


we obtain, from equations (22) and (23), 



or, in feet and seconds, approximately 



From the figure and by assumption 2, 

Q:H-j8=y = 7r— y. (19) 

Again by assumption 2, 

yt=(V/Va)\a. (20) 

Noting that 


R = + (T - tf) V, 


t } 


and that 

V = V 4- V 

and adding vectors around the circuit. 


Ro + TVs = tf\ a + tf\w + (T — tf)Yt ; 
or, by virtue of equation (20), 

R„ + rv. = + [TF, + (Va - F,)</] y ■ (21) 

L a 

For solution in terms of y it is most con- 
venient to take components along and normal 


tan /3 = tan ^o(l— ^ ) , (29) 

\ cos p J 

or 

tan (3 = tan jSo (l — 12 -/l + tan^ js) . (30) 

The forms of equations (29) and (30) should 
be convenient for certain purposes, but they 
must be reworked for an explicit solution. 
Transforming equation (30), and squaring. 


tan^ jS — 2 tan jSo tan (8 + tan^ /So 

= 12^ (1 + tan^ /3) tan^ Po, 
or 


/tan p Y 
\tan PoJ 


tan Po 


122 (1 + tan2 p), 


or, again 
(1 - 122 tan2 Po) 
Solving this for 


/tan p Y 
\tan PqJ 


^ tan p ^ ^ 

2 — + 1 - 122 = 0. 

tan Po 


we have 


tan P = tan Po 


tan P 
tan Po 


1 - /l - (1 - 02) (1 - tan2 ft) 


1 - O'' tan^ ^0 


(31) 




iNFIDENTIAL 


94 


AIMING OF TORPEDOES FROM AIRPLANES 


When Qw = 0, for no wind, ^ = io 


tanjS = tanjSo 


1 -/l - (1 - {§) (1 - ipHan^ M 
1 — tan^ jSo 


When ^0 = 0 there is no correction for air 
travel, and both equation (31) and this one 
reduce to 


/3 = /3o, 

except for the relatively unimportant case 
where Va = Vt, which must be specially 
handled. 

Equation (31) gives tan ^ in terms of tan 
and the composite wind and air travel correc- 
tion O. It is also possible, and in many cases 
more opportune, to offer sin jS in terms of O 
and sin /3o, where 


sin/3o = fis sin a (fis = 12'). 
Returning, then, to equation (29), and mul- 
tiplying by cos /3 we have 

sin/3 = tan (cos /S — 12), (32) 

or 

sin jS + 12 tan /3o = tan j/ 1 — sin^ /3 ; 
squaring and rearranging. 


sin^ /3 -j- 212 sin jSo cos /So sin /S — (1 — 12^) sin^ /So = 0 . 
Solving this equation as a quadratic in sin yS, 
sin/S = — 12 sin /So cos /So 

+ sin^/So cos^/So + (1 — 12 2 ) sin^/So ; 

and finally 

sin/S = sin/So (<f/ 1 — 12^ sin^/So — 12f/ 1 — sin^/So)- 

For no wind, 12 = io- For no air travel correc- 
tion whatsoever. 


sin /S = sin /So. 


6 8 LINKAGE FOR IMPLICIT RANGE 

CONVERSION 

We referred above to a simple linkage solution 
for the present-range problem. Having shown 


the proposals for computation by successive ap- 
proximations, and having given the more com- 
plex explicit expressions of the last section, we 
now show the basis of the simpler procedure 
which was subsequently employed for all di- 
rectors having present range as an input. 

We refer to equation (31) above, and to the 
accompanying Figure 14. The uncorrected lead 



angle /So is assumed to be obtained in the usual 
way, as for example from equation (26) above. 
Assume, for convenience, that the wind correc- 
tion is unnecessary, so that 12 reduces to |. It 
is now geometrically evident that by the choice 
of unit length as indicated in the figure, and the 
enforced parallelism, that equation (31) is em- 
bodied by virtue of the similar right triangles 
completed by the construction lines. The com- 
puting linkage follows readily from this di- 
agram. 


, CONFIDENTIA] 


Chapter 7 


AIMING OF BOMBS FROM AIRPLANES 


7 1 OUTLINE OF DEVELOPMENT PROJECTS 

W E LIST FIRST, approximately in historical 
order, and aside from the relative em- 
phasis they will receive elsewhere in this chap- 
ter, all except the most trivial of the bombing 
projects in which we have engaged for NDRC. 
Subjects related to guided bombing are omitted, 
since these are treated exclusively in Chapter 8. 
Our activities have been on the following topics : 
bombing aspects of the airborne torpedo, and of 
similar experimental projectiles; hand-held 
bombsights, principally for low altitude, includ- 
ing those specially prepared for antisubmarine 
attacks, as well as those for use in blimps, and 
extending to the theory and development of the 
special angular rate methods; computers for 
ground speed as an aid in bombing operations of 
several types ; computers for slant range at re- 
lease ; computers of the auxiliary type known as 
preset for advance adjustments in synchronous 
high-altitude bombing ; computers for statistical 
evaluation of the optimum length of train in 
terms of tactical and instrumental circum- 
stances ; modification of high altitude techniques 
for increased effectiveness with incendiary 
projectiles; instrumental developments for toss 
bombing; theoretical work on the errors in- 
curred in low-altitude bombing by comparable 
techniques ; theoretical work on flight paths on 
which release may occur over an interval, on the 
angular-rate principles which may then be used 
as criteria, and on the special cases for climbing 
approach and for vertical dives to which these 
paths reduce; and on certain model equipment 
for training purposes. 

The most prominent projects, on which effort 
was expended on a considerable scale, were those 
for the various hand-held bombsights, for error- 
analysis of low-altitude methods, and for a com- 
puter to be used in a toss bombing system (as a 
component, in fact, of the pilot’s universal 
sighting system: Project PUSS, NO-265). 
These projects will be discussed more fully than 
the rest, and Section 7.4 will therefore be de- 


voted to them in this chapter, in company also 
with certain related theoretical work not hith- 
erto promulgated. The rest, comprising a good 
number of smaller endeavors, coordinated in 
some cases with the work of other groups, we 
shall discuss first in somewhat broader terms 
and with one eye on historical sequence and sig- 
nificances. 


7 2 VARIOUS RESEARCHES - A 
COMPENDIUM 

We had not discussed, in our prefatory com- 
ments, or elsewhere heretofore, the general plan 
of this report, beyond pointing out that it was 
to be of flexible arrangement, being composed 
substantially of a set of independent mono- 
graphs. For a specific reason this is not the case 
in a strictly literal sense ; and we explain : Chap- 
ters 1 through 5 have dealt with techniques and 
components which have applied more or less 
horizontally over the various fields of aiming- 
control development. In Chapters 6 through 10, 
the individual developments and problems of 
these latter fields are considered in sequence, 
vertically. References are natural between these 
two groups of chapters, representing as they do 
the two distinct modes of presentation. Thus, 
in several cases, a technique, treated in the ear- 
lier group in general, has been there illustrated 
as applying to a development justifiably assign- 
able to the latter group. It is natural, in such a 
case, that reference be later made to the previ- 
ous discussion or exposition. The attempt will 
be maintained, however, especially in connec- 
tion with material which is considered worthy 
of preservation, to avoid the obvious failing 
whereby such subject matter may be inade- 
quately treated through reciprocal reference to 
another context for amplification; and on the 
other hand we shall not indulge the temptation 
bodily to reproduce a given exposition in more 
than one spot on the thesis of complete inde- 
pendence or self-sufficiency for each monograph. 


95 




CONFIDENTIAL 



96 


AIMING OF BOMBS FROM AIRPLANES 


A slight apology is offered, incidentally, for in- 
cluding this explanation here, but it serves thus 
as a reminder to the writer at a juncture where 
a rather scattered account of general activity 
is begun. 

To return to bombs, it seems as though we 
had been preoccupied right from the beginning, 
from our beginning at least, with trajectories, 
their calculation, their approximation, or con- 
triving to suit them in some sense or other. 
Bombs are only one example. Torpedoes falling 
through the air furnished several problems in 
which we became involved. Questions on this 
score concerned the relations between their air 
trajectory with respect to the air and the same 
trajectory measured in water coordinates. These 
relations were important partly because the 
water-entry characteristics depended on the 
alignment of the torpedo itself with its water 
coordinate trajectory, and partly because the 
aiming problem properly must be solved in rec- 
ognition of the entry position as well as of the 
compass direction to which it is automatically 
steered following such entry. Again, the effects 
on the air travel of glide and skid must be con- 
sidered, since neglect of these produces errors 
which are found significant in practice. The abil- 
ity of the torpedo to resist impact and turning 
torques on entry further placed restrictions on 
the bombing aspects of its use. Underwater 
trajectories, or orbits as they have come in some 
cases to be called, are naturally crucial for tor- 
pedoes and relate closely to their air travel be- 
havior ; such properties after entry as the 
'‘hook,'' so called, and the turning radius by 
which the torpedo comes over to its set course, 
are important to the aiming problem. The de- 
tails of behavior underwater arise also for the 
airborne depth charge, such as used against sub- 
marines, and for the plunge bomb.^ In rockets, 
as used against shipping, a predictable and ef- 
fective underwater trajectory is one of the most 
important desirables, and the character of such 
trajectories, as well as those in the air, affects 
the design of aiming controls. We are discussing 
such controls, for depth charges and for rockets, 
in another place. The case of the plunge bomb 
is less related to other work, however. This mis- 
sile was not to be self-propelled, either in the air 

“Proposed by Slichter. 


or in the water, but was to be so designed aero- 
dynamically and hydrodynamically as to have 
most nearly ideal properties in both media. 
Model studies had shown that very long and flat 
underwater orbits were attainable by special 
shapes, and the plan was to make a projectile 
of large pay load ratio which would also be 
simple to handle strategically, or logistically. 
High-speed launching was considered, in either 
horizontal or climbing approaches, to attain 
great range.^ 

In any bombing problem the speed of the 
launching vehicle with respect to the air is far 
less important than its speed with respect to 
the ground, or ultimately with respect to the 
target. Yet it is the airspeed which is available 
by local measurement. The synchronous bomb- 
sights invoke an implicit measurement of speed 
in target coordinates for the principal part of 
their solution, applying airspeed only for the 
aerodynamic trail corrections and so on. In other 
methods of bombing, wind and target speed may 
require estimation by the operators, so that 
their joint effect, with airspeed, on the ground 
speed or on the speed in target coordinates may 
be measured. Even where wind, for example, 
may successfully be determined in intensity and 
direction, and this requires either a saltier pro- 
ficiency than is typically at hand or a time-con- 
suming series of maneuvers, the corresponding 
process of vector addition is very difficult in an 
emergency, and seldom, in any case, leads to 
high accuracy. For such reasons we were led, as 
others have been, to the development of mechan- 
ical computers for these quantities, that is for 
airplane speed with respect to ground and tar- 
get, which would be compact and simple to op- 
erate, and which would offer improvements over 
the then available rather large and clumsy plot- 
ters. One such project was for a ground speed 
computer to be used in connection with hand- 
held low-altitude bombsights which were simul- 
taneously in development. This computer ac- 
cepted airspeed, wind speed, airplane heading, 
and wind direction; it gave not only ground 

•’We worked with Dr. Slichter on the question of 
aiming controls for such a bomb, and computed proba- 
ble errors using a variety of the available sights, 
standard and experimental. The whole proposal ap- 
peared to be worth more than a little attention, but 
no construction was ever resorted to in our branch of 
this item. 


VARIOUS RESEARCHES— A COMPENDIUM 


97 


speed, but by a later attachment, the drift 
angle. Four experimental versions were built, 
leading to the final one which was produced to 
the extent of twenty units. The resulting in- 
strument was considered quite successful in 
meeting the specifications laid down. It was 
mountable almost anywhere, even in the most 
restricted confines, and could be operated very 
quickly with one hand, even when wearing a 
heavy glove. A geometrical vector principle was 
involved, with a single sliding linkage, and the 
setting scales were cylindrical and coaxial. In 
one form a miniature, rotatable ship model could 
be attached to aid in computing the additional 
course change required by target speed. A re- 
port on this item is listed in the bibliography 
appended to the present chapter. 

Another ground speed computer, of very dif- 
ferent sort, was designed by the writer in 
answer to an expressed need by Wright Field 
Armament Laboratory and H2X radar research- 
ers. The problem was to provide, in a horizontal 
bombing approach at known altitude, the 
ground speed — or target speed — by means of 
two successive measurements of the slant range 
to the target and of the time intervening be- 
tween them. A novel nomogrammic method was 
applied, and drawings for the resulting manual 
computer were supplied.® A model was built and 
tried out by the 20th Air Force. 

For low-altitude blind bombing, in which 
BuAer desired a rough and ready means to bomb 
on the radar range signal, a manually operated 
computer was built which provided the slant 
range at which release should occur. Inputs were 
altitude and closing speed, both measurable by 
'‘blind” methods. Altitude came from the radio 
altimeter, and closing speed from the range rate 
at ranges great in comparison to the altitude. 
The instrument which resulted, being extremely 
small and flat, and operable with one hand, was 
considered successful as specified, but was anti- 
quated almost immediately by the development 
of other techniques. 

For higher altitudes, that is to say above 
5,000 feet, a somewhat more ambitious develop- 
ment program was undertaken to construct 
computers as auxiliaries to the synchronous 
bombsight. In this work we cooperated in a 

'To Captain F. Best. 


more general program with the Aircraft Re- 
search Section of BuOrd, with whom in fact 
most of our airborne developments were coor- 
dinated. The principal auxiliary instrument in- 
volved thus has been the so-called preset com- 
puter, of which three separate developmental 
models were prepared. In operation, these com- 
puters were either attached to the auxiliary 
(vectorial) ground speed computer of the Nor- 
den bombsight or, as in one case, they were to 
be of the hand-held variety. The original idea 
was to enable a preliminary and approximate 
solution of the bombing problem, on the ap- 
proach, so that either this solution could be 
employed as such if the synchronous method 
proved impossible or inappropriate, or to permit 
initial settings in the synchronous mechanism 
which would lead more rapidly and/or more 
precisely to an effective attack therewith. An 
added requirement, of the preset-computation, 
was to inform the operator of the moment at 
which, after maximum delay for evasion and 
so on, he must begin his synchronous operation. 
To the existing ground speed computer, which 
normally accepted airspeed, wind speed, and 
wind direction (the latter being subsequently 
maintained by the azimuth stabilizer of the 
bombsight) , and which was sometimes em- 
ployed for low altitude bombing independently 
of the synchronous instrument, was added a 
target speed component wherein the course and 
speed of a ship target could be set. Stabiliza- 
tion applied then both to the wind and target 
speed vectors. From this component of the sys- 
tem an approximate drift angle could be de- 
rived, for initially guiding the pilot, and, most 
significantly, a measure of the closing speed was 
obtained. The latter, as a mechanical displace- 
ment, fed the preset computer. Manual settings 
were made of altitude, time of flight, trail, and 
bomb type; reference to bombing tables being 
admitted since this was necessary, anyhow, for 
the synchronous bombsight itself. (Several 
projects for mechanizing the tables were known 
of, and it is evident in retrospect that this would 
not have been difficult. A complete linkage com- 
puter for this purpose, combined with the pre- 
set computer, could probably have been readily 
prepared, with the application of techniques 
described elsewhere.) The output of the preset 


OfFIDENTIAL 


J 


98 


AIMING OF BOMBS FROM AIRPLANES 


computer, which was essentially a geometrical, 
or triangular, representation of the well-known 
bombing formula, consisted in two scale read- 
ings. One was the tangent of the probable drop- 
ping angle, to be set into the bombsight via the 
‘"rate” knob. The other was the tangent of that 
target angle, as observable on the bombsight 
angle-indicator, at which synchronous control 
should begin. Computation of the latter was 
made through recognition of the (adjustable) 
time interval during which synchronization 
could effectively be performed, and interpreta- 
tion of this interval in terms of the correspond- 
ing (and displaced) value of the tangent of 
target angle. The first models having been large 
and flat, subsequent models were very much 
more compact. Tests were made at NAS Banana 
River.<* * The results were reportedly satisfac- 
tory, but production was not planned at last 
knowledge. 

In collaboration with AMP,® and the Statis- 
tical Research Group at Princeton, a study was 
made of instrumental application of work they 
had done on the optimum length of train, or 
the interval between successive bombs in a 
train. Several computers were experimentally 
prepared, based on slide rules which were pre- 
sented, which permitted settings of : number of 
bombs, altitude, probable dropping error, dimen- 
sions or type of target, and the angle of ap- 
proach thereto. The answer appeared as the 
displacement in space between adjacent bombs, 
this being set, together with the airplane speed, 
on the intervalometer. Various models of the 
computer, in which several compromises oc- 
curred between ease of setting and compactness, 
were prepared. One model was directly attach- 
able to the intervalometer itself, so that the 
spacing which was computed would be delivered 
automatically to that instrument. 

Following requests from more than one 
source, a certain amount of work was done on 
the question of dropping incendiaries from high 
altitudes. The classical bombsights were unus- 
able owing to the excessive trail of these bombs, 
which surpassed the limits of the mechanism. 
It was desired in particular to drop both high 
explosives and incendiaries on the same spot. 

“In cooperation with (then) Lieutenant H. G. Cooper. 

*Principally with H. H. Germond. 


This is evidently possible through the regular 
bombing procedure, applied, say, by a syn- 
chronous bombsight for the standard projectile, 
followed by a regulated maneuver and subse- 
quent release of the incendiaries, which, then, 
if the solution was correct, arrive at the target 
somewhat later. Knowing the time of flight and 
trail for the standard bombs, and also those 
properties under the circumstances of the at- 
tack for the incendiaries, it was shown how to 
compute, by a determinate vectorial solution, 
the course change and the added time interval 
to come to the secondary dropping point after 
the initial release was made. This solution was 
shown personally to several interested persons. 
Subsequently a similar solution to the problem 
was heard of, apparently found by independent 
search. 

A certain amount of thought was given by 
the writer to a particular method of bombing.^ 
This method, which at first glance may seem 
somewhat naive, came to be called Zenith- 
Bombing or “Z-Bombing,” and involved a pre- 
cipitate diving approach from directly above 
the target. The plan was to make the path with 
respect to the target extend vertically over the 
latter, for then the in vacuo solution would be 
exact, and the trail would be quite small owing 
to the small horizontal component of airspeed. 
Of course the path in the air mass would be 
inclined, in the presence of wind, and conse- 
quently the heading itself would be out of the 
vertical in general. One problem is how to as- 
sure, if indeed it is essential, that the airplane 
is not “upside down’^ in such circumstances. On 
the instrumental side, a good (although special) 
gyro horizon would be the basic mechanism, ac- 
curacy otherwise depending on the variables of 
the problem only to a second order. Dynam- 
ically, it is most important to arrange for stable 
subsidence to the vertical dive, and numerous 
measures have been considered conjecturally for 
this purpose, including those involving the ap- 
plication of angular accelerometers. One ad- 
vantage, probably only temporary, was consid- 
ered to be the practical difficulty experienced 
by typical gun emplacements at the target, say 
a warship, in firing straight up. This would not 

^Discussed at length with Commander E. S. Gwath- 
mey of BuOrd. 


« 


^ONFIDENTI 


CLASSICAL METHODS AND INSTRUMENTS 


99 


deter support fire in quite the same manner, 
however. 

A project was undertaken at The Franklin 
Institute on the development of a maneuverable 
target for the standard cart type of bombing 
trainer. In such training it had been common 
practice to simulate a ship target by means of 
a “bug’" which was driven along the floor in a 
straight line at adjustable speed. It was con- 
sidered that a generalized “bug’' could be made 
which, under the choice of an instructor, could 
execute turns as would a ship under attacks. 
Such turns are not strictly arcs of circles, un- 
less a continuous series of turns is made, or un- 
less the rudder has been held still for some time, 
so that the intermediate transitional character 
of the evasion had also to be represented.^ Six 
models of the final version, which was rather 
luxuriously supplied with selective controls, 
were recently completed and delivered. 

CLASSICAL METHODS AND 
INSTRUMENTS 

The adjective classical is meant here to imply 
horizontal bombing at medium and high alti- 
tudes, although all techniques in this field are 
not old ones. Generalization to bombing in non- 
horizontal flight, while not trivial, is straight- 
forward for reasonable climbs and glides, 
provided the motion is unaccelerated. The dis- 
tinction between low and high altitude bombing 
is principally determined by whether or not trail 
may be neglected. We may state the classical 
principle of bombing in terms of what happens 
to a standard bomb when it is dropped. In air 
coordinates, it falls down and forward in the 
vertical plane containing the instantaneous 
flight path at the instant of release. Its down- 
ward progress is slower than in vacuo, either 
the total time from any altitude, the time of 
flight, that is, or the difference between this and 
the time of flight in vacuo, called the differen- 
tial time of flight, being given by known func- 
tions of altitude and airspeed. Its forward 
progress in the air mass is merely the product 
of airspeed and time of flight, from which is 

^Lieutenant H. G. Cooper, at NAS Banana River, 
who had taught bombers special methods for bomb- 
ing targets evading in this manner, tried out the 
products of Project BUG as they were prepared. 


rectilinearly subtracted the so-called trail dis- 
tance, or trail, at least for the whole drop, this 
trail being also known as a function of airspeed 
and altitude. In ground or target coordinates, 
one need only add the motion of the air, or the 
wind. All standard bombing theories are the 
direct result of these facts, but a few special 
results may be pointed out. In vacuo, and when 
‘flying horizontally, it is only necessary to fly in 
the invariant vertical plane containing the tar- 
get and to drop the bomb when the target ap- 
pears at an angle from the vertical whose 
tangent is the square root of 2V^/(gh), V being 
the airplane speed in target coordinates. The 
arrival at this condition may be determined on 
the basis of many other relations, as when the 
slant range is the square root of 
or when the absolute angular rate of the target, 
in radians per second, is the reciprocal of 
{2V/g) + (h/V). Other complications enter, 
even in vacuo, when one wishes to hit a point by 
aiming at an auxiliary point somewhat removed 
therefrom, or when it is desired to aim the 
center of an automatically spaced train of bombs 
by releasing the first such bomb. 

Removing the vacuum restriction, which is a 
poor first approximation at all but the lowest 
altitudes, we may see that the travel of the 
bomb, as viewed from above, is given in ground 
coordinates by the vector sum of the following 
displacements: the vector velocity of the air- 
plane in the air, or the airspeed vector, multi- 
plied by the time of flight; the vector velocity 
of the air (assumed uniform) with respect to 
the target, or simply the wind vector, multiplied 
also by the time of flight ; and the trail distance, 
or else the trail angle multiplied by the altitude, 
taken in a direction opposite to that of the air- 
speed vector of the airplane. The trail or trail 
distance is the horizontal displacement of the 
bomb behind the unaccelerated bomber at im- 
pact; the trail angle is this displacement di- 
vided by the altitude. This angle is usually 
measured in mils, whereas properly speaking 
this is the tangent of an angle. Both trail, 
whether distance or angle, and time of flight, 
for any given projectile horizontally released, 
are functions of altitude and the scalar airspeed. 

For any given target, as may be shown di- 
rectly from the above facts, there is a vertical 




confidentia; 


100 


AIMING OF BOMBS FROM AIRPLANES 


cylinder which determines the locus of release 
points and directions of flight for a hit. The axis 
of this cylinder, at target level, is upwind from 
the target a distance equal to the wind speed 
multiplied by the time of flight of the bomb. Its 
radius is the product of the bomber’s airspeed 
and the time of flight, minus the product of the 
trail angle and the altitude. At the instant of 
dropping, the airplane must be head toward, or* 
have its airspeed vector directed toward, the 
axis of this cylinder, and it must then also be 
just piercing the surface of this cylinder. These 
conditions are both necessary and sufficient for 
a hit on the target, following the premises al- 
ready given. Simultaneously, the ground track 
of the bomber must pass through a point at tar- 
get level which is also upwind from the target, 
but displaced from by a distance given by the 
product of the altitude, trail angle, and wind 
speed, divided by the airspeed. It will be seen 
that this latter point and the previous cylinder, 
as bombing ''directrices,” are independent of 
the angle of approach of the bomber. 

The solution of the Norden Bombsight Mark 
15 is based inherently on the above geometry, 
with one major approximation however. In this 
bombsight, the full trail distance is taken geo- 
metrically along the ground track rather than 
along the airspeed direction. Since the one is 
the other multiplied by the cosine of the drift 
angle, usually less than 15 degrees, the ap- 
proximation is a good one. While it might have 
been equally simple, as indicated once by J. B. 
Russell of Section 7.2, to build an exact mecha- 
nism, the point is not too serious. In the Norden 
Mark 15, the closing speed, or ground speed for 
a stationary target, is obtained as an angular 
rate, being inherently divided by the altitude, 
by synchronously tracking the target through a 
tangent screw. The "range” solution is expres- 
sible, on the basis of data already given, as 



where </>o is the dropping angle, v/h is the ratio 
of closing speed to altitude (or the absolute 
angular rate of the target as though directly 
beneath), tf = tfih,Va) is the time of flight, 
and T = r{h,Va) is the trail angle. In some 
other types of bombing, particularly w^here 


solutions are obtained by correcting the first 
order vacuum solution, the "range lag” is used 
instead of trail or trail distance, being defined 
as the distance the bomb falls behind a vacuum 
trajectory at impact. The relation between 
range lag Re and trail distance hr may readily 
be shown by equating two expressions for 
tangent of dropping angle as above. Thus 



and hence 

Re= hr — V (if — tfc) (2) 

where tfc = ^2gh is the vacuum time of fall. 

7 4 THE EXTRAPOLATING 

ANTISUBMARINE BOMBSIGHT 

The instrument referred to is a bombsight 
specifically intended for low altitude use 
against submarines, allowance being automati- 
cally included for underwater travel of the 
target in case of submergence at any instant 
during the attack. While the sight is meant to 
be hand held, it is not necessarily restricted to 
such operation.^ 

A number of experimental models have been 
built, under our contract at The Franklin Insti- 
tute, of which many were given preliminary 
tests in the air against a dummy target. Produc- 
tion of 75 units of the final model, which became 
bombsight Mark 20, was undertaken. Wide dis- 
tribution to Fleet units was made. 

Representatives of BuOrd and BuAer were 
freely consulted on this project, which was 
assigned the project-control designation NO- 
129} 

The geometrical development of the extra- 
polating solution for underwater travel of the 
target is shown in Figures 1 through 8. In 
Figure 1, an attacking airplane A is approach- 
ing a surfaced submarine S; the submarine 
is headed at an angle a to the line of sight. If 

’‘The principle on which this instrument and its 
method of use are based is due to Captain A. B. 
Vosseller of ComAirAsDevLant. Section 7.2 cooper- 
ated with him in a development project for reduction 
to practice of this principle. 

‘Commander E. S. Gwathmey of BuOrd and Cap- 
tain Vosseller were liaison officers for the Navy. 


t 


CONt'lUEN'l'UL 


1 


THE EXTRAPOLATING ANTISUBMARINE BOMBSIGHT 


101 


the submarine remains on the surface, at least 
until the airplane arrives to within bombing 
range, then the problem is relatively simple. 
This possibility will be considered below, as a 
special case of the more general problem. If 
the submarine submerges, for example at 5, 
then it is necessary on the one hand to be able 
to fly a course passing over it and on the other 


larly justifled. If the above assumptions are 
made and the variable conditions known, then 
it is evident (Figure 2) how the airplane 
course may be altered, through a discoverable 
angle ^ and at the time of submergence, so 
that subsequent flight on a straight track will 
result in the desired ‘^collision course” passing 
over the submerged target at B. While the 


PROJECTION OF GROUND TRACK 


Figure 1 



S 


\ 

\ 



to have a criterion for the release of bombs at 
the appropriate point on such a course. After 
submergence the only visible reference available 
for these purposes is the temporary but sta- 
tionary swirl left on the surface by the 
submarine. 

It will be assumed that the airplane had been 
navigating directly toward the submarine at 
the moment of submergence, that is, the track 
of the airplane was directed toward the target 
at that time. It will also be assumed that the 
following conditions are known: target aspect 
angle a at submergence, target speed Vg under- 
water, altitude H, and ground speed Vg of the 
attacking airplane (although in different con- 
texts, the symbols h and i7, for altitude, are 
used interchangeably throughout this chapter 
and, probably, elsewhere) . The underwater 
target speed is taken as an empirical constant 
of the instrument. The supposition that the 
target does not appreciably alter its direction 
during or shortly after submergence is simi- 


triangle ASB, of which a and /? are angles, is 
a space triangle, these angles are equally well 
represented in any similar triangle. It will be 
evident below how the turning angle (3 is given 
directly by the mechanism. 

While a knowledge of the range at submer- 
gence is not necessary, usable values being 
limited principally by persistence of the swirl, 
bomb release must take place at a deflnite range 
from the collision point B in Figure 2. The 
dropping range RB depends on the ground 
speed Vg and altitude H, assumed constant, 
of the attacking plane at release, for the for- 
ward distance covered by the bomb is Vgtf, 
where tf is the time of flight. Thus if distance 
is everywhere measured in feet, and time in 
seconds, we have 

RB = V,t, = 

4 

Since there is nothing to distinguish the point 
B on the water surface, and thus to guide the 


ONFIDENTIA 


P 


102 


AIMING OF BOMBS FROM AIRPLANES 


release of bombs, it is an essential feature of 
the method to determine the range RS (Figure 
3) from the swirl at which release may occur. 

If time is measured from the moment of 
submergence (and of the assumption by the 
airplane of a collision course), release may be 
said to take place after the arbitrary interval 
T. The total time intervening between submer- 
gence and arrival of the bomb will be T + tf, 
and the distances traveled respectively by air- 
plane and target will be Vg(T tf) and 
VsiT tf) . At the time of release the target 


quately be allowed for by a correspondingly 
small delay or forward displacement. The ac- 
cumulated corrections for these effects are con- 
tained in the removal, by the distance L, of the 
point R (Figure 4), to the new point F. The 
line segment FD is then taken as the fictitious 
range, which becomes equal to the real range 
ES when E arrives at F, both segments being 
then equal, within a good approximation, to 
the desired dropping range FS from the swirl. 

Mechanization of the principle involves two 
triangles, a “horizontal” one and a “vertical” 



Figure 4 


will be at the point C (Figure 3), having trav- 
eled a distance VgT and with Vgtf yet to go. It 
is evident that the triangle RGB is similar to 
the triangle ASB. If the moving point D is in- 
troduced (Figure 4), leaving C at the instant 
of submergence and moving backward toward 
S at submarine speed, it will arrive at S at the 
precise moment that point E, representing the 
airplane and leaving A simultaneously at air- 
plane speed, arrives at R. Thus the line RD 
(which might be considered as the fictitious 
dropping range from the swirl), and the line 
ES (the real swirl range) , become simultane- 
ously equal to the actual dropping range from 
the swirl. Equality of RD to ES, then, may be 
used as a criterion for release. Thus if the 
triangle RDB were mechanized, to scale, with 
the leg BD growing out from BC at the appro- 
priate rate, and the angle RDB appropriately 
set, it will generate the “range” RD which, by 
its momentary equality to the real range from 
the swirl, will signal the instant of release. 

In practice, single bombs are not generally 
used, so that in order to lay the stick sym- 
metrically across the target the first bomb 
must be released at a point one-half the stick 
length back along the track. Furthermore, the 
underwater travel of the bombs, as they pene- 
trate from the surface to the depth set for det- 
onation, must be accounted for by an addi- 
tional backward displacement at the release 
point. The small amount of trail may ade- 


one. The horizontal triangle, as shown in 
Figure 5, is derived directly from the geometry 
of Figure 4. In this triangle the leg FB is 
known, as is the portion BC of the leg BD. 
The remaining portion CD grows uniformly 
in time. The angle a' (Figure 5), the supple- 
ment of angle FBD, is set to the observed 
course angle a, to which it is a satisfactory ap- 
proximation since the difference /? is always 
small. It will be noted that the angle rep- 
resented as angle CRB in Figures 3 and 4, is 
still available in the known configuration of 
Figure 5. The vertical triangle of the mechani- 
zation, shown in Figure 6 as GFD, has a com- 



REAL RANGE AND SLANT 
RANGE AT TIME t 


Figure 6 

mon leg (FD) with the horizontal one. It serves 
as a means for comparing the fictitious range 
with the real range. If the altitude leg GF is 
made equal (or rather proportionate) to the 




ONFIDENTI 


THE EXTRAPOLATING ANTISUBMARINE BOMBSIGHT 


103 


real altitude as shown in the “real’' vertical 
triangle GES of Figure 7, the equality of FD 
and ES is indicated by equality of the fictitious 



Figure 7 


depression angle <f> = GDF of the mechaniza- 
tion to the real depression of the swirl. Thus 
if the triangle is held (even approximately) in 


rectly at the swirl. A less accurate method, 
although easier to explain, is to point GD at 
the swirl and merely note when the leg FD 
becomes horizontal. This procedure is diagram- 
matically shown in Figure 8, although it is not 
usable with a bubble as level indicator owing 
to the response lag. 

For convenience of adjustment and for com- 
pactness of instrumentation, the two triangles 
shown separately in Figures 5 and 6 and to- 
gether in Figure 9 are subjected to a scalar 
transformation which consists merely in divi- 
sion of their linear dimensions by the time of 



a vertical plane containing the swirl, and FD 
is accurately horizontal, release may occur 
when the fictitious slant range GD points di- 



DIVIDE BY 


Figure 9. Components of bombing triangles for 
mechanization. 


flight tf, or by VH/4. The resulting pair of 
triangles (Figure 10) completes the mechani- 
zation, at least symbolically. Altitude {H) and 



Figure 10. Components of bombing triangles for 
mechanization. 


ONFIDENTIAL 




104 


AIMING OF BOMBS FROM AIRPLANES 


ground speed (Vg) are set in manually, sub- 
merged submarine speed (F^) being assumed 
constant; the angle a or a', described above, is 
set in by direct comparison with the target 
being approached while on the surface. The 
range correction, L' in the transformed ver- 
sion, is taken to be preset in dependence on 
stick length, bomb characteristics, etc. Begin- 
ning upon manual operation of a trigger at 
submergence, the variable leg of the horizontal 
triangle grows at a rate determined by set al- 
titude as shown in Figure 10. The hypotenuse 


ters the problem as it affects the ground speed 
as compared with airspeed, the difference be- 
tween these two values varying drastically with 
compass heading. Ground speed is a necessary 
adjustment in the bombing instrument. There 
are a number of ways to satisfy these various 
conditions, each involving some sort of guide 
by which the pilot may head his plane to pre- 
pare for and carry out the bombing run if and 
when submergence takes place. 

If wind speed (assumed known in magnitude 
and direction) is added vectorially to airspeed. 


/ 

UNDERWATER 



Figure 11. Mechanization of guiding apparatus for approach in azimuth. 


of the vertical triangle defines a ‘‘fixed” line 
of sight to be directed at the swirl. The release 
depression is determined through a bubble as- 
sembly attached to the base of that triangle. 

As to actual operation, this method is based 
on a straight run over the target, which is en- 
tered upon at the moment of submergence. It 
is required that the ground track for this run 
be oriented by the angle ^ (Figure 2) with re- 
spect to the line of sight to the submarine (or 
swirl) at the time of submergence. If ground 
speed {Vg) and the target angle a were already 
known and set into the instrument, and if the 
plane's track were headed toward the sub- 
marine up to the time of submergence, it would 
merely be necessary to turn in the direction of 
target heading through the angle as indi- 
cated by the instrument, and thenceforth to 
hold a constant course. A change in heading 
itself by the amount ^ would accomplish this 
to within sufficient accuracy. In the presence 
of wind, however, it may be difficult for the 
pilot to “navigate” in this manner, that is, to 
direct his ground track at will. Wind also en- 


as in Figure 11, the true ground speed is given. 
Thus if the wind vector is stabilized, automati- 
cally or by compass matching, the proper head- 
ing for any given ground track may be directly 
determined. If, furthermore, a “submarine” 
vector is added to these two (wind and air- 
speed), and similarly stabilized after orienta- 
tion, the proper heading may be directly se- 
lected by which to “lead” the target right up 
to the time of submergence. A simple computer 
of this sort was prepared for use by the pilot 
in connection with this method, and also pro- 
vided the value of ground speed for setting in 
the bombsight. 

The initial models were fairly straightfor- 
ward physical adaptations of the geometry of 
Figure 10. The combined triangle pair formed 
three consecutive edges of a tetrahedron (see 
also Figure 12), the “vertical” edge being nor- 
mal to the plane of the other two. The assembly 
appeared and was operated somewhat like a 
sextant, and was built around a timing clock 
of which the rate was adjusted to an altitude 
scale and which was triggered off upon sub- 


♦ 


fONFIDENTIAL 


THE EXTRAPOLATING ANTISUBMARINE BOMBSIGHT 


105 


mergence. Two link lengths were adjustable, to 
altitude and ground speed scales (and a sub- 
sidiary stick length scale), and the angle be- 
tween another pair of legs was set according 



Figure 12. Three-dimensional form of bombing tri- 
angles. 


to target aspect. A ring and bead sight was 
used, each component at one end of the con- 
nected series of links. Ring and bead separa- 
tion was variable as the adjustments were 
made and as time elapsed. The signal for re- 
lease was given by a bubble attached normally 
to the vertical leg. In one of the models the 
bubble image was collimated and reflected into 
the line of sight by a somewhat elaborate me- 
chanical and optical structure. None of the 
early models were particularly easy to use, es- 
pecially in an airplane under working condi- 
tions. Two hands were continually required, 
and determination of lateral verticality and 
bubble transit left much to be desired. Several 
desirable features were sacriflced in order to 
minimize load on the timer, and some intricate 
and bizarre mechanism was resorted to for the 
avoidance of blind spots. Withal these first 
two-models showed the workability of the prin- 
ciple and formed reductions to practice from 
which much information and experience was 
gained. 

In subsequent models it was decided to re- 
tain the principle intact but to change the de- 
sign radically. It appeared possible, and at 
length practical, to incorporate the whole sight 
in a hand-held, pistol-grip affair which might 


be completely operated, including adjustment, 
with one hand. In particular it was found to 
be possible to fix the line of sight with respect 
to the body of the instrument, making the task 
of sighting considerably simpler. This involved 
building the mechanism “around the line of 
sight,^^ and separating the two triangles at 
their common leg. Aimed exactly like a pistol, 
the signal for release appeared automatically, 
as the passage of the target by the aiming 
point, with the instrument so held that the 
transit of a bubble indicates the proper de- 
pression. A bomb-release key is incorporated 
as a pistol grip for the sight, so that release is 
made by a trigger in full analogy with the 
firing of a pistol. Adjustment of target aspect, 
altitude, and ground speed, and initiation of 
the timer operation at submergence, could all 
be carried out with the thumb of the same hand. 

As was mentioned above, this antisubmarine 
bombsight, which became Navy bombsight 
Mark 20, was placed in limited production on 
the basis of the final experimental bombsight. 
Extended flight tests prior to such production 
had established that, with care, horizontal low- 
altitude bombing, in the altitude range from 
100 to 500 feet, could be carried out to a prob- 
able range error of 20 feet, which was as good 
as could be done in line, or laterally. This was 
with a nonsubmerging target. Few tests ac- 
tually were carried out, owing to mechanical 
difficulties, under simulated conditions of sub- 
mergence, and it is not known whether enemy 
submarines were successfully attacked, either 
on or below the surface, with this equipment, 
although a number of models were distributed 
to the various operating theaters. For this pur- 
pose a set of instructions was prepared^’^ and 
certain Navy officers were assigned to educa- 
tional trips in this connection. 

While the practicality of the general method 
was established, a number of modifications 
were proposed and carried out which omitted 
the underwater extrapolation feature. One such 
model included an inherent vector computer for 
the combining of airspeed and wind speed 
and/or target speed for a more effective solu- 
tion. Auxiliary devices such as the miniature 
ground speed computer, mentioned elsewhere, 
were prepared for cooperative functions with 


7 


CONFIDENTIAL 


106 


AIMING OF BOMBS FROM AIRPLANES 


such bombsights. In some of the experimental 
hand-held bombsights, the ranges of airspeed 
and altitude were considerably extended, the 
latter up to 1,000 feet. One of these sights, par- 
ticularly for use in blimps, extended to very 
low airspeeds. This model, which became bomb- 
sight Mark 24, was tested at Lakehurst with 
better results, it seems, than might have been 
expected. 

A project which resulted in a technique much 
used in other fields was that for automatic 
setting of altitude, in the Mark 20 type of sight, 
from the radio altimeter. Here a d-c servo was 
employed, with motor and resistive follow-up 
mounted on the hand-held instrument, accept- 
ing as altitude a voltage from the AYD al- 
timeter. Since the “triangular” bombing prin- 
ciple employed in the sight depended rather 
crucially on this variable, this accurate and 
automatic setting from the AYD altimeter gave 
very impressive bombing results during tests. 
The tests, incidentally, were over water. 

7 5 METHODS INVOLVING ABSOLUTE 
ANGULAR RATE 

Development of hand-held bombsights based 
on the “triangular” principle was gradually 
discontinued for several reasons, although the 
results were not to be disparaged. In the first 
place better principles were at hand. Further- 
more, the submarine emergency was waning, 
and rockets were the more popular weapon any- 
how. This is not to say that low-altitude bomb- 
ing was not important, for it remained so 
throughout and its previously unexpected tac- 
tical application has been one of the phenomena 
of the war. It was a curious circumstance 
which led high-altitude bombing to be well de- 
veloped, at least instrumentally, when World 
War II began, whereas the apparently simpler 
art of low-altitude bombing, which in fact was 
put to extensive use, was almost completely 
unequipped. 

Many competitive bombing methods had also 
appeared, such as the FM radar Sniffer, which 
gave a solution in terms of range and altitude 
to the target, even on blind approaches, and 
which was later generalized to gliding attacks, 
with the range rate and the rate of change of 


altitude as input variables. There were also 
other bombsights of the visual triangular va- 
riety. The most impressive new principle, per- 
haps, was that of angular rate bombing, which 
we have also discussed in Chapter 3. This 
principle was of British origin, being employed 
in their Mark III LLBS, in which a grid of 
lines at infinity were rotated downward in 
space by means of a luminous rotating helix 
and a stabilizing mirror system. With the tar- 
get observed through the image of this grid, 
release was made automatically when relative 
motion momentarily became zero. It was sug- 
gested by the present writer that this principle 
could also be embodied the other way around, 
by tracking the target accurately and measur- 
ing continuously the angular rate in space of 
the physical index with which the tracking was 
carried out. We were thus led to apply, at first 
to hand-held sights and later to those which 
were supported in various ways, rate meters 
based on captured gyros of the type previously 
being developed for lead-computing applica- 
tions. This type of instrument came to be 
known as the BARB. Under our immediate di- 
rection a project was conducted in which 
strain-gauge torque measurement was applied 
to captive gyros for this purpose. A number of 
such models were built and tested (see Chap- 
ter 3) . The most successful such method, how- 
ever, has been that involving the pneumatic 
capturing technique, which indeed has been 
experimentally applied in other fields of fire 
control, to captive gyros and to other compo- 
nents, and which was developed principally un- 
der Section 7.3 by intersectional arrangement. 
In the research on the pneumatic angular rate 
bombsight, which ultimately became the bomb- 
sight Mark 23, and of which a subsequent 
elaboration — called SuperBARB — having a 
pneumatic form of aided tracking has recently 
been designated the Mark 27, several agencies 
contributed.^ (See Chapters 3 and 4 of Volume 
1, Division 7.) 

Whereas in Chapter 3 this angular rate prin- 
ciple of bombing is described somewhat, we 
may give here a slightly different interpreta- 
tion of the basic doctrine. We refer thus to the 

jExcellent theoretical work was contributed by 
L. Goldberg of the McMath-Hulbert Observatory. 


PATHS OF CONSTANT RELEASABILITY 


107 


accompanying Figure 13. In target coordinates, 
it is evident that the angular rate of the ap- 
proaching bomber, as seen from the target, 
which is the same as that of the target from 



Figure 13. Illustrating angular rates on bombing run. 


the bomber, is (v/h) sin^c^. As a function of 
time, this is evidently 

where v is the closing speed and t is the time 
before crossover. The release condition, in this 
simplest case, is obtained by substitution of 
the time-of -flight t/, in terms of altitude, in this 
equation. The more general cases^ develop 
when an offset in aiming-point is desired, when 
climbs and glides are contemplated, and so on. 
It is found, for example, that this method, at 
the lower altitudes particularly, is remarkably 
insensitive to errors in the altitude input, and 
is also less sensitive, relative to other methods, 
to errors in the closing speed. 

At one time it was planned to base a syn- 
chronous bombing method, in which the whole 
prerelease tracking interval would be utilized 
to develop accuracy, on matching the time func- 
tion given above for the angular rate to an 
analogous function of frequency, which is well 
known in an RC electrical circuit. It is clear, 
however, that the tracking scheme of Super- 
BARB, though based on another synchronous 
principle, has been quite successfully executed, 
as indicated by recent test results. With what 
has been said here, together with the various 
references given®>^ the interested future in- 
vestigator will find enough to carry him rea- 
sonably far into this subject. For the present 


writer, the most significant application of the 
absolute angular rate principle, to instrumen- 
tal solutions for gravity drop, is in the com- 
bined system of PUSS, where, particularly in 
the rocketry case, this principle is applied si- 
multaneously to the gravity drop correction and 
to the lead computing solution, employing thus 
the same fundamental gyro component. 


7 6 PATHS OF CONSTANT RELEASABILITY 


For conjectural bombing tactics it is of in- 
terest to study those paths on which a bomb 
may be released at any instant, each such hypo- 
thetical release scoring a hit. We consider here 
the problem in vacuo, and with respect to a 
coordinate system fixed in the target. It is fur- 
ther assumed that the airplane speed, in target 
coordinates, is constant. The results obtained 
have been used as flight criteria in several other 
investigations. 

It is evident that any given such path must 
be completely contained in a vertical plane 
through the target. Let denote the co- 

ordinates of a point of release resulting in a 
hit. Then 


dxo 

(3) 



(4) 


where tf is the time of flight of the bomb and 
dxo/dt, dijo/dt are the values of the components 
of the projectile’s velocity at the instant of re- 
lease. Since dxjdt and dyjdt are also the 
components of the plane’s velocity at this in- 
stant, then for constant velocity v on the flight 
path (in target coordinates) 



(5) 


Elimination of tf between equations (3) and 
(4) gives 


2/0 = Xq 


dyo / dt 
dxo / dt 



or 


dyo gxo^ /dxo\-^ 


(0) 


POKFIDENTIA: 


108 


AIMING OF BOMBS FROM AIRPLANES 


Since from equation (5) 


/^\-2 _ r /^Y 1 
\dt) ~ I ^ \dxo) J ^ 


(7) 


mine c let (Xo^Vo) be the point at the begin- 
ning of the dive where rj = 0. Then 


the expression ( 6 ) can be written with no time 
derivatives as 




:^o, 


and thus 


2/0 


dyo gx^ 
dx^ 2v^ 


[-(£)■]- 


(8) 


= — y sinh-i?;^ 


(14) 


(15) 


The desired constant speed dive bombing paths 
are the loci of the point (Xo,yo) satisfying 
equation ( 8 ). Hence the subscripts are now 
dropped and equation ( 8 ) becomes the differ- 
ential equation of the paths. 


y = X 


,dy gx^r ,/dy\ 2 l 

dx ' 2v‘^\_ \da;/ J 


Equations (15) and (11) constitute the equa- 
tions, with ry as a parameter, for the dive bomb- 
ing paths. 

By setting t] = 0 in these equations there is 
obtained, as a special case, the level bombing 
criterion in vacuo 


(9) 


This equation is inconvenient to integrate 
as it stands. Substitution of 


22/0 — = Xo\ 

g 


(16) 


gives 


dy 
~ dx 


gx^ 


XV + (1 + 

2v^ 


( 10 ) 


( 11 ) 


For a given speed v and altitude y, equation 
(16) gives the point for entering the dive path 
continuously. If </> is the depression angle of 
the target viewed from the plane then 


cot <f> 




Differentiation of equation (11) with respect 
to X results in 

dv QX , qx^ dv 

V = V + X + {I V^) + V 


2^ 

gyo 


(17) 


or 


dx 


^ 1 ^ . 
dx 

^ vx 

g 


dx 


This can be written as a linear first-order dif 
ferential equation in x: 

vyg 


gives the depression angle at which the dive 
may begin. Release may occur at this or at any 
subsequent point on the path. 

Since 

ry = tan 7 (-90° ^ 7 ^ 90°) (18) 

where y is the angle from the horizontal to 
the tangent to the flight path. Equations ( 11 ) 
and (15) may be written as 


dx V 
dv 1 + 


gx 

y ^ xtany + — sec^ 7 
2v^ 


( 12 ) 


1 + v‘^ 

Solution of equation (12) by the standard 
formula gives 


V2 


— In (tan 7 + sec 7 ) 

_l 

sec 7 


(19) 


( 20 ) 


_ \ r r 

"J i+v^ I J 1+772 


x = e 

g 


l+V^ dr] 


or 


1 + r 


+ c 


-h 

--a + v^) 

g 


(1 + 772 ) dv^c\ (13) 


= — - (1 + 772 ) " (sinh-i 77 + c) , 

g 

where c is a constant of integration. To deter- 


^(xo-xsecy) 

= tan 7 + sec 7 . ( 21 ) 

The flight path terminates at the target, as 
might be expected, for by equation (19) y 
approaches zero with x. At the origin the flight- 
path angle 7 has a value 71 given by 


Xo = — In (tan 71 + sec 71 ) , 

g 


(22) 




3DNFIDENTIAL 


THE DIVING ATTACK IN GENERAL 


109 


or 

g _ 

e = tan 71 + sec 71 . (23) 


As seen in Figure 14, there are two branches 
involved in the solution. Beside the normal 
diving path, there is a climbing path on which 
release at any point will also result in a hit. 


Thus 


6 73^0 + e , 

sec 71 = = cosh 

From equation (16) 




— xo = 2 ~ = 2 tan < 


Xo 


and hence 

sec 71 = - 
Similarly 

771 = tan 7i 
Since 


2 tan <Ao 


+ e 


-2 tan 00 


= sinh ( — Xo ) = 

\V2 / 


= cosh 2 tan </>o. 


sinh 2 tan <f>o. 


tan 0 = - > 

X 

equation (11) can be written as 

tan2 0 = 77 tan 7/ (1 + 772) ; 

2v^ 


or 


gcot,^= 

1 + 772 

Similarly, from equations (14) and (16) 


g 


— y cot 0 = 

V2 ^ 


4/1 + 772 

Taking these last equations together 
tan 0 == 77 + (tan 0 o — i sinh“i 77) //l + 772 , 



Figure 14. Path of unvarying releasability at constant 
(26) bomber speed. 


This branch approaches as a limit the zenith 
over the target. While a valid bombing path, 
it is of undetermined practicality. 


which gives the relation between the tangent 
of depression angle and the slope 77 of the flight 
path at every point. Equation (25) shows that 
when y approaches zero, the limiting values of 
the slope angle and the depression angle are 
the same: 

tan 01 = 771, (28) 

so that by equation (24) 

tan 01 = sinh 2 tan 0o. (29) 

Of the constants involved, the fundamental 
ones are: speed v of plane, altitude at be- 
ginning of dive. The rest, Xo, 0o, yi, are 
derived from these. 


7 7 the diving ATTACK IN GENERAL 

There are several practical reasons for want- 
ing a method of dive bombing different from 
those, elsewhere mentioned, which lead to ap- 
proach paths on which release may take place 
arbitrarily over an interval. Naturally it would 
be desirable oh the face of it to obtain this type 
of approach, and angular rate methods are 
available to provide highly articulate aiming 
criteria for this purpose, since then it would 
not be of critical concern at what particular 
instant release took place. Errors in the choice 



DENTI 



no 


AIMING OF BOMBS FROM AIRPLANES 


of the release instant, or in the releasing 
mechanism itself, would be of little conse- 
quence, provided only that the path were stably 
held to. However, it appears that such paths 
are not the easiest to fly, for while they are not 
strictly bomb trajectories (see above) they are 
paths on which the lift force essentially dis- 
appears, and an unfamiliar mode of operation 
of the controls must be learned and resorted 
to. It is recognized, of course, that this circum- 
stance need not be fundamental, and might be 
altered by the proper design of airplanes or by 
appropriate training techniques. But another 
practical difficulty arises. For a large useful 
region of range, glide angle, and speed, the 
downward visual freedom of most existing 
airplanes is not great enough that the target 
is visible to the pilot at the moment of release, 
or, if the airplane is following a path of un- 
varying releasability, in the time interval over 
which release may occur. This is admittedly a 
property of airplanes, as such, and as in the 
previous objection does not necessarily carry 
permanent status. Thus it is hardly impossible 
to arrange for such downward visibility, since 
certain nonflghter airplanes, and proposed 
fighter types as well, do have this feature in 
relatively high degree. But both of these points 
have had at least temporary significance, and 
have militated against bombing tactics involv- 
ing continuous releasability on the approach. 
We note that while not completely so restricted, 
such tactics would in general be associated with 
diving attacks. 

It must here be interpolated that the prop- 
erty of lack of criticalness, or tolerance, of the 
choice of release instant would not belong ex- 
clusively to tactics in which the release path 
were rigorously followed. Other approaches, 
in which, for example, less curvature may be 
involved, and on which consequently a reason- 
able lift may still be experienced, will pass 
somewhat gradually through a condition of 
releasability, and in these of course the choice 
of the release instant is also, relatively to other 
methods of bombing, noncritical. We refer 
again to the bombing solution of the Army A-1 
multipurpose, or Draper/Davis, sight. This 
system involves an approach of the above char- 
acter, and should be studied by the serious 


student. The present writer is not qualified to 
represent this system in detail. 

Several methods have been proposed and de- 
veloped which avoid the practical difficulties 
above named, and which achieve accuracy in 
spite of losing the tolerance of release instant 
which follows upon the release-path philosophy. 
These methods involve, first, a diving approach, 
in general, during which the target is visible 
more or less straight ahead, then a suddenly 
imposed upward curvature of path during 
which the target becomes invisible to the pilot, 
and during which also the bomb is automati- 
cally released through a computation depend- 
ing on the properties of the previously held 
path and on the character of the pull-up 
maneuver. One such method^ was developed 
in the so-called DBS system, for BuOrd and 
later on British orders. In this system an 
approach was made by proportional navigation, 
to compensate for target motion in the air 
mass, and automatic release during the pull-up 
regime was effected by simultaneous compu- 
tation of the accumulated pitch, the airspeed, 
altitude, acceleration, and the glide angle pre- 
viously held. Glide and the accumulated upward 
turn were delivered by specially arranged 
gyros, and a nomographic type of computer, 
with mirrors and photocell, embodied the de- 
sired criteria for automatic release. The initial 
approach course was guided by a free gyro 
moving a mirror in the sight head, giving a 
delayed approach to a collision course in a 
manner referred to in Chapter 1. 

A somewhat similar method which has re- 
ceived much recent attention and develop- 
mental effort, and which has been employed 
also for the gravity drop solution with other 
projectiles than bombs, was that originally 
proposed.^ The term toss bombing came to be em- 
ployed for the technique involved, although de- 
scriptively, or rather externally, the tactics 
referred to above, or again with the DBS, were 
substantially employed. That is, this term 
might be applied to several methods, although 
its connotation has been limited to those in 
which a special type of release computer was 

’'Devised by M. Alkan, the French fire-control ex- 
pert and instrumentalist, erstwhile of Specialties, Inc. 

’By (then) Colonel Morton of Army Ordnance. 


THE DIVING ATTACK IN GENERAL 


111 


employed. Toss bombing instruments, such as 
the so-called AIBR, were made to depend on 
the indication of an integrating accelerometer, 
sensitive in the direction of the airplane’s ver- 
tical, which was allowed to begin integration 
at a point shortly prior to the pull-up, for bomb 
release. Thus was measured approximately the 
velocity impulse imparted to the bomb in a 
direction upward, against gravity, and normal 
to the line of sight to the target. Release oc- 
curred, through simultaneous computation of 
the duration of bomb flight, which was made, 
for example, by measurements on range or 
altitude and various speed, when the upward 
impulse being increasingly imparted was suf- 
ficient to compensate for the downward pull of 
gravity, to be accumulated during the time of 
flight. Inherent advantages arose from the 
method of integrating acceleration, since then 
fortuitous irregularities of flight, following 
initiation of the final computing phase, were 
automatically accounted for, and variations 
between flight path (measured in space) and 
the airplane axis were of second-order impor- 
tance to the accuracy. Correction for target 
motion in the air mass, requiring something 
more nearly a collision course than the typi- 
cally employed straight pursuit, was not con- 
templated until rather recently. It has been 
planned, including the toss method, with in- 
tegrating accelerometer, in the PUSS system, 
to apply a correction for target motion."^ 

Whereas the earlier AIBR was based on a 
theory of horizontal approach to the target, as 
in plane-to-plane bombing, and was modified 
for the gliding approaches which were appro- 
priate against targets on the ground, the theory 
as proposed for PUSS was built anew in par- 
ticular recognition of this latter approach as 
the significant one. Continuous measure- 
ment was planned of altitude, airspeed, normal 
acceleration during the earlier phase, and the 
integral of the incremental normal acceleration 
during the pull-up phase. It was determined 
to prepare a small mechanical computer to 
assess the release condition in terms of these 

“Proposed by H. Pollard of AMG-C, who has been 
responsible for the form of computation and the 
theory of the method as developed thus far for PUSS. 


variables and automatically to initiate release 
of the bomb. For acceleration and the integral 
thereof, a pneumatic component was developed 
comprising a captive mass, a feedback inte- 
grator, and a valving assembly whereby the 
various initial conditions could be imposed as 
desired. Both the acceleration, exponentially 
averaged, and the instantaneous integral of the 
incremental normal acceleration were delivered 
as rotations, to the mechanical computer, by 
pressure motors responding to, or incorporat- 
ing, these variables as generated by the pneu- 
matic components. Airspeed and altitude were 
similarly delivered to the computer by capsule 
diaphragms. This toss bombing computer, 
called PACT, is to be combined integrally in 
the PUSS system described in Chapter 10. It 
will share inputs with other components of that 
system, and the mechanical-linkage computer 
it embodies will be physically adjoined to that 
of PUSS. Also theoretically developed and 
studied^ is the instrumental method for use 
with PACT, as part of PUSS, whereby the ap- 
proach in the first phase is so guided with 
respect to the target that motion of the latter 
is compensated for. This method involves a 
function also of the gravity-drop compensation 
of the computer, in elevation, and in azimuth 
employs a unique principle whereby the proper 
path for “kinematic lead” is very rapidly sub- 
sided to. Embodiment of the latter principle 
is made by specializing the function of the 
PUSS rocketry computer to give a double over- 
correction in airplane heading for changes in 
direction of the line of sight to the target. 
Technically, in the jargon of lead-computing 
sights and deflecting gyro systems, the crite- 
rion^^ in azimuth is: a = 1. In elevation, the 
sight head is undeflected, the line of sight being 
along a direction normal to the computing axis 
of the accelerometer.® 

“By H. Pollard. 

“For further details, and a better technical discus- 
sion, the writings of H. Pollard of AMG-C should be 
referred to. Some of these are given here in the bib- 
liography. 

In Pollard’s work, as in Alkan’s, the non-circular 
nature of the pull-up path, in practical circumstances, 
is recognized. 


FIDENTIA 


Chapter 8 


CONTROL OF GUIDED BOMBS 


» 1 REVIEW OF ACTIVITIES 

A ll our work in this field was pursued 
-either through the machinery of coopera- 
tion between NDRC Divisions 5 and 7 or 
directly in an advisory capacity for the former 
division. There is no hope for separation be- 
tween the activities which occurred under each 
such sponsorship, since the interweaving has 
been most complete, so that no attempt at such 
separation will be made. We were first engaged 
on controls for guiding the RAZON bomb, fol- 
lowing the issuance of a memo by the Director 
of OSRD in which he outlined computing meth- 
ods which might be employed for that purpose, 
and in which he referred the problem in part 
to the fire-control experience of Division 7. 
(See also Volume 1 of Division 5.) The writer 
was made responsible for the establishment 
and conducting of a development program for 
preparation of experimental equipment in 
realization of these methods, which program 
was carried on largely between the contractors 
of Division 5 and those of Section 7.2 in Divi- 
sion 7,^ 

Aside from minor consultation and partici- 
pation in conferences, the visual or optical 
phase only of the RAZON, and as a special case 
the AZON, guiding problem was treated by us. 
Without describing the RAZON bomb in detail, 
since this is an affair principally of Division 5, 
we may say that it is the modification of a 
standard 1,000- or 2,000-pound bomb in which 
a special tail assembly replaces the standard 
fins. The assembly comprises intact: radio re- 
ception for steering by rudder and elevator, 
gyro component for roll stabilization, movable 

‘In the former case, notably, there was Gulf Re- 
search and Development Corporation and certain con- 
tracting agencies at MIT, while for the latter The 
Franklin Institute was the locale of operations and 
supplied personnel and other developmental facilities. 
In the more recent stages, L. N. Schwien Engineering 
Corporation of Los Angeles, under contract to Divi- 
sion 5, was involved for several reasons, not the least 
being that H. A. Van Dyke, who had been project en- 
gineer at The Franklin Institute in this connection, 
transferred his employment there. 


rudder, elevator and aileron with “muscles'^ 
for the latter controls, and a flare for visual 
identification of the missile during the drop. 
Two general types of guiding were contem- 
plated. In the first, the bomb was guided from 
the dropping airplane in such a manner that 
its trajectory terminated in the target, cor- 
rections being applied only as necessary owing 
to errors in dropping which would prevent 
its unguided trajectory from terminating in 
that manner. In the second proposed method, 
either through special maneuvers of the air- 
plane or through a program of control applied 
to the bomb, the plan was to make the bomb 
align itself collinearly between the bomber and 
the target during the latter portion of the time 
of drop. In both cases the process was similar 
in one respect, in the azimuthal deflection 
problem, to the guiding of AZON, in which 
one dimension only was corrected and which 
was applicable particularly to long and narrow 
targets attacked approximately in the direc- 
tion of their greatest dimension. The second 
method for guiding RAZON, in which it was 
proposed to attain temporary collinearity by 
visual guiding, was discarded when it became 
evident that sufficient maneuverability was not 
available in this projectile. This question in it- 
self was a large one, involving aerodynamic 
design of the missile — several variants and 
predecessors of RAZON were also considered 
— and we used both numerous analytical and 
differential analyzer solutions in assisting with 
its study. With this conclusion, and subsequent 
experimental corroboration, attention was 
turned to controls for the noncollinear guiding 
technique. Starting from the Bush proposals 
and others^ a design was pursued of an optical 
sight and computer, which eventually became 
the CRAB sight, to permit the guiding opera- 
tor to carry out his mission simply by the 
superposition, under control, of a pair of in- 
dices. As it turned out, these indices were, in 
fact, images of the target and of the flare on 


‘’Already advanced by J. P. Molnar at Gulf. 




CONFIDENTIAL 


J 


112 


REVIEW OF ACTIVITIES 


113 


the bomb. Whereas a completely special com- 
puter and optical system were first under de- 
velopment, it became suddenly apparent to us 
that the same function could be embodied in a 
relatively simple modification of the Norden 
bombsight, which could then be used following 
the original drop of the bomb, as a normal 
type, to assist in the guiding process as a con- 
tinuation of its normal operation. Remarkably 
enough, the whole operation of the bombsight 
was kept usefully in service for this post-release 
purpose of computing and presentation. The 
operator merely transferred his attention from 
the synchronizing controls to those for guiding 
the bomb, and from the alignment of cross 
hairs on the target to the alignment thereon 
of the bomb flare as the latter was in flight. 
It was thus only necessary to modify the trajec- 
tory in small and gradual degree; the para- 
boloidal character thereof was in general re- 
tained. Accuracy, assuming the guiding itself 
to be expertly and stably carried out, depended 
only on the time of flight setting in the Norden 
computer. For employment with this technique, 
the addition to the bombsight consisted only in 
the attachment of a small mirror, the so-called 
CRAB mirror, to the objective of the telescope 
of that instrument. 

We have mentioned the use of the differential 
analyzer in this study. It was employed again 
for further developments as described below. 
In the CRAB project, a number of other aids 
were pressed into service, however. Aside from 
rather elaborate space-models in which the rela- 
tionships among trajectories, bomber paths, 
and other geometrical objects were made evi- 
dent, electronic simulators (Chapter 4) were 
constructed and applied to learn of the stabil- 
ity and effectiveness of the guiding process as 
such. These instruments not only gave informa- 
tion in highly tangible form which applied to 
the development of controls, including indeed 
those controls locally installed on the projec- 
tiles, but served later as training aids for civil- 
ian and Service operators in the field. 

A subsequent activity constituted a return 
to the struggle for collinearity conditions 
toward the end of the drop. This struggle was 
tied up in a curious manner with the question 
of evasion, or of maneuvers indulged in by the 


bombing airplane following the release point. 
While such maneuvers might reduce the danger 
over the target area, they also imposed serious 
problems in guiding. Study was given to this 
problem, partly with the idea that a simple 
instrumental correction could be applied, pro- 
vided of course that the evasive tactics did not 
prevent seeing the target at all. We had found 
it unlikely that the RAZON bomb, including its 
various modifications, and even though the air- 
plane followed special paths in a vertical plane 
— as in the case of an analogous German 
weapon — could be made satisfactorily to fol- 
low a trajectory which would give collinearity 
with the target over a terminal time interval. 
Further with regard to evasion, it was dis- 
covered that there did, in truth, exist a natural 
evasive path which also assisted in meeting the 
criterion of terminal collinearity. For bombs 
only a small fraction more maneuverable than 
the standard RAZON this technique would 
probably have led to successful flare guiding 
on the collinearity principle as described. Al- 
though no field experiments were made, all the 
data for the study has been derived from dif- 
ferential analyzer solutions. The procedure con- 
sisted in a normal and rather sharp, or well- 
banked, steady turn by the bomber to one side, 
while the projectile is guided somewhat to the 
other side of the original range direction, the 
approach having first been made along a 
ground track displaced from the target on the 
side toward which the evasive turn is made. 
Thus the region near the target, where pre- 
sumably antiaircraft fire might be heaviest, is 
avoided as completely as possible. In the guid- 
ing operations, which are added to an auto- 
matic program which curves the trajectory to 
one side and into a gradually increasing dive, 
by first curving the trajectory less, and then 
more than would be done by gravity alone, the 
manual controls can concentrate, at least 
toward the latter part of the drop, on holding 
the flare superimposed on the target in true 
physical collinearity therewith. For several 
reasons, however, this method was not tried 
out. One was that the ROC bomb, having re- 
portedly about three times the maneuverability 
of the RAZON, came to be considered for visual 
flare guiding. It developed actually to have 


114 


CONTROL OF GUIDED BOMBS 


somewhat less maneuverability, in terms of the 
potential normal acceleration under guiding. 
Since the greater maneuverability was avail- 
able, special maneuvers to attain collinearity 
were not considered essential. From that point, 
no further study was given to evasion. Many 
bombers continued their runs anyhow, with 
standard bombs, and it was felt by some that 
the additional danger involved, even, ideally, 
from the point of view of the personnel, would 
be worth the continued straight run during the 
time of flight, in terms of targets successfully 
reduced, if such tactics made it possible to guide 
effectively. Such remarks apply, of course, to 
AZON as well. 

The ROC bomb, which we shall not describe 
in detail either in the present brief review or in 
subsequent sections of this chapter, was in- 
tended as a television seeker for ground targets, 
to be manually controlled in steep drops. Its 
maneuverability was attractive for the collinear 
type of flare guiding, and while the television 
(MIMO) component was still in preparation 
authorization was obtained to try out this mis- 
sile for that purpose. A computing sight was 
constructed, involving a generalization of 
CRAB which brought about gradually, and 
maintained, identity between the reflected flare 
image and the actual flare image toward the 
latter part of the time of flight. This sight was 
called CARP, and it was also an adjunct to the 
bombsight Mark 15, from which it derived 
automatically several vital inputs. Although its 
manual operation was somewhat more complex, 
and this in fact prevented its unmitigated suc- 
cess in experimental trials, this operation was 
in general analogous to that of CRAB.<^ As we 
have already said, electronic simulative meth- 
ods were applied, for these flare guiding de- 
velopments, for the construction of study 
models, humanly operable, in connection with 
questions of the stability and the practicality 
of the guiding processes. On a further applica- 
tion of these same methods, the study models 

"While the instrumental part of this project was 
conducted at first at The Franklin Institute, as a col- 
laborative venture between Division 7 (Section 7.2) 
and Division 5, H. A. Van Dyke being project engineer 
for the contractor, it was moved to L. N. Schwien 
Engineering Corporation under Division 5, at about 
the time testing was to begin, since Van Dyke became 
employed by the latter organization. 


were modified into prototypes for trainers in- 
tended for field application, which were then 
produced and further modified through other 
facilities of Division 5. 

Another major application of electronic sim- 
ulation has been to the control of ROC with 
MIMO, fundamentally a '‘seeking,” or “hom- 
ing,” or “automatic interception,”*^ problem 
which was subsequently studied. This study was 
conducted by the writer.® The status of the 
study was actually that of collaboration or more 
properly of consultation with Division 5 and 
their contractors, principally Douglas Aircraft, 
on their developmental control problems in con- 
nection with the television bomb. Contrary to 
the general impression, it is not a trivial mat- 
ter, given a falling bomb with remotely manip- 
ulable control surfaces, and the means for see- 
ing ahead along the bomb's axis via a television 
camera, precisely to guide the bomb to any 
given target at ground level. Among others, 
there are two principal circumstances here 
which make the problem appreciable. One is 
the motion of the landscape, in the televised 
image, which results from pitching and yawing 
motions of the projectile not directly connected 
with the curvature of its air path. The other 
arises when steering is so performed that the 
missile heads directly or approximately toward 
the target. By virtue of this constraint the 
curvature of flight must progressively increase 
as the range decreases, provided the target has 
lateral motion of appreciable magnitude in the 
air mass. We note that the latter type of motion 
is equally occasioned by wind as by proper 
motion of the target on the ground or over the 
water. In the ROC projectile, the response of 
the image to pitching and yawing is reduced 
by the purposeful and considerable, although 
experimentally not yet complete, reduction of 
these motions by appropriate design of the 
projectile. This design, which involves a sym- 

‘’By connotation, these terms have become badly 
confused, and their usage is widely disparate among 
various groups. A purer though more esoteric lan- 
guage has been developed by W. B. Klemperer, whose 
many writings on these and allied topics should by all 
means be consulted. 

"With the assistance of R. M. Peters and L. Julie, 
the latter being responsible for the laboratory simu- 
lative equipment thus em’^lbyed at Columbia Univer- 
sity. 


REVIEW OF ACTIVITIES 


115 


metrical and articulate wing structure, permit- 
ting independent alignment of the central body, 
is significant for future such projectiles, es- 
pecially when self-propelled, but it is not the 
function of this report to give a technical de- 
scription hereof, since such material will be 
found elsewhere in very complete form.^ Both 
for the television application and for the flare 
guiding application mentioned above, ROC (or 
ROKH) was roll-stabilized by the same means 
as were AZON and RAZON, and the character 
of this means and of the resulting space be- 
havior of the missiles, in the sense of rigid-body 
dynamics, is further discussed below since this 
question enters the problems of trajectory 
analysis and synthesis. The control artifices for 
the remote, human guiding of the television 
ROC, or MIMO-ROC, were outlined in Chapter 
4. In the development and study of control dy- 
namics and equipment for this type of guiding, 
and of the stability and effectiveness of such 
equipment under the proposed tactics of opera- 
tion, we were naturally advanced considerably 
by having previously studied the air trajec- 
tories of this and other guided bombs. For ex- 
ample, we were by now familiar with the 
dynamic and transient properties of such tra- 
jectories, for the artificial embodiment of which 
both the differential analyzer and electronic 
simulative methods had been employed. It was 
thus approximately known, for the television- 
bomb work, which of the rationalizations, and 
guides to judgment, were valid in the predic- 
tion of control performance. Continued applica- 
tion of simulative equipment^ allowed us to 
assess the several proposals which had been 
made for control dynamics, and to select one 
arrangement which appeared superior from an 
overall standpoint. A conclusion was also pos- 
sible, by this means, on the degree of precision 
with which it would be required to adjust the 
dynamic constants of the regulatory dynamics 
which were recommended. 

^We refer to NDRC Division 5, and to the Douglas 
contract. 

^Our own research involved electronic models, 
whereas mechanical and optical models, some of fan- 
tastic intricacy and ingenuity had previously been 
proposed and designed. In some cases partial models 
of the latter variety were available for corroboration, 
short of full-scale tests, of the results attained by 
the electronic simulators in our laboratories. 


One other major activity in the field of guided 
bombs concerned the technique of GCB, or 
ground-controlled bombing, in which a radio 
link allowed control, from a position on the 
ground relatively adjacent to the target, of a 
bomb dropped from a vantage point overhead.’* 
The visual phase of the weapon, in which a flare 
was to be attached to the bomb, was principally 
considered by us. Again we were aided by a 
prior knowledge of the behavior of the projec- 
tile in flight — in this case the RAZON bomb 
— and of its response to control signals, by 
virtue of prior experience with synthetic and 
analytic studies made on the differential analy- 
zer and with other aids to computation. We 
should not by any means imply that no trajec- 
tories were computed by numerical integration, 
for these processes were earlier conducted in 
this general connection by ourselves, and more 
extensively by others. This procedure, however, 
gave all the better appreciation of the improved 
facility for study and invention provided by 
the automatic forms of mathematical operation. 

A theory of guiding was worked out, in terms 
of a pair of ground stations from which the 
falling bomb would be visible in its downward 
course toward the target, whereby the trajec- 
tory could be gradually modified so as to 
terminate, without serious warpage toward the 
lower end, in the target. Several alternative 
mechanisms were proposed which embodied 
such theory, and these were discussed in nu- 
merous conferences with the other personnel 
concerned. Certain compromises were arrived 
at in which the best features of widely differ- 
ing proposals were reasonably well preserved 
in the forms finally determined upon for joint 
recommendation. It appeared that, with the aid 
of simple control equipment, and under circum- 
stances that admitted of considerable flexibil- 
ity, the technique of GCB could probably be 
carried out with great success, both as to the 
ease with which the manual phases of the 
process could be learned and applied, and as to 
the accuracy with which refractory enemy ob- 
stacles and strongholds could thus be reduced. 

*'In the study of this problem the writer, and 
R. M. Peters of Section 7.2 who assisted him, worked 
most directly with H. A. Van Dyke of L. N. Schwien 
Engineering Co. 


116 


CONTROL OF GUIDED BOMBS 


« 2 ANALYSIS AND SYNTHESIS OF 

TRAJECTORIES 

A right-handed Cartesian coordinate system 
is assumed in the air mass, with origin at 
ground level directly beneath the point of re- 
lease of the bomb, and the positive x axis is 
taken in the same direction as that of the veloc- 
ity vector of the airplane with respect to the 
air at the instant of release. (See Figure lA.) 



BENEATH DROPPING POINT 


Figure 1A. Coordinate system and general guiding 
space. 

The only forces acting ordinarily, on the un- 
guided missile, are gravity and the drag force 
D, directed oppositely to its velocity vector V 
with respect to air. Deflection of the control 
surfaces introduces a sideways force S per- 
pendicular to V but otherwise as yet undefined 
in direction, and a lift force L perpendicular to 
both D and S. 

Then the equations of the trajectory are 

nx = Dx “h “1“ Lx 

my = Dy Sy Ly (1) 

mz = Dg Sz Lx — mg , 

where m is the mass of the bomb, g is the 
acceleration of gravity, and the subscripts x, 
y, z indicate components of the forces in the 
directions of the coordinate axes. Assuming 
that the forces D, L, and S vary with the square 


of the velocity, these equations can be written 
in the form 

i = dv^^ + sv^^ + W ^ 

Jj b L 

y = + + (2) 

z= dv^~ -|- Iv'^ ^ — g 

D ' S L ^ 

where 

d = d{8E,8R,z) = — ^ Cd{^e,8r) 

7Yl Jj 

s = s{Sn,z) = -^Cs{Sr) (3) 

m 2 

1= l(dE,z) = —^Cl{^e)- 
m 2 

The drag function d depends, as indicated on 
the two (as yet incompletely defined) com- 
ponents 8e and Se of the CSD, (control-surface 
deflection), measured from the neutral position 
of no control. A is some area^ proper to the 
bomb; p is the density of air at the altitude z; 
and Csy Cl, and Cd are the appropriate aerody- 
namic coefficients. Owing to symmetry, Cs and 
Cl are identical functions of Sr and Se respec- 
tively, while Cd depends on both Sr and Se- It is 
assumed that Cl, and hence L, is independent 
of Sr, and vice versa. In the case of both rudder 
and elevator control Cz, (8£?,8/;) is obtained from 

Cd(^e,8r) = Cd(0,Sr) + Cd(^e,0) — Cd(0,0). 

Again, owing to symmetry, Cd is the same func- 
tion of Se as of Sr- 

The gyro stabilization (see Figure 2) of the 
bombs in question insures that the lift force 
vector (scalar magnitude L) remains always 
parallel to the vertical plane in which the bomb 
was projected. The departure from this assump- 
tion is so small that Ly may be taken as always 
zero. Since D, L, and S are mutually perpen- 

‘In AZON and RAZON, the convention was to use 
the cross-sectional area for this quantity. In ROC it 
appears as the wing area. 


ANALYSIS AND SYNTHESIS OF TRAJECTORIES 


117 




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s=e-«KE( 8 E) 


Figure IB. Differential analyzer connections for guided bombs. 


f 


rONFnJENTIAL 



dw d t 


: 


118 


CONTROL OF GUIDED BOMBS 



Figure 2. Gyro arrangement for roll stabilization. 

dicular it follows that the direction cosines of 
D, L, and S are 

—X Dy _ —y 

D + ’ D + ’ 

_ —z 


Or, setting 

_ ^2 _|_ ^2^ i;2 _ ^2 y2 _j_ ^2^ 

we have 



y = V {—dy + 8u), 



( 6 ) 


The use of the differential analyzer at MIT to 
solve these equations was obtained through 
NDRC Division 7, and later Division 5, con- 
tracts. Appropriate constants have been used 
which apply to the various RAZON types. 
Later, solutions for the several sets of ex- 
perimental ROC constants were possible. It 
was initially found impossible to get the com- 
plete equations on the analyzer in the case of 
three-dimensional control. In the case of 
“range-only” control, in the vertical plane 
purely, the exact equations could be used. 
For the former case, in three dimensions, the 
following approximate equations were found 
to suffice and were used. 


X 






— z 




^ -f- ^2 z 


_ 0 ^ _ 


■xy 


Sy // X^-\-', 


(4) 


^ i/x^-\-y^-\-z^^x‘^-\-z^ S |/^ 2 _|_ 2_|_22 


S j/ x‘^-\-y^-\-z^^ x‘^-\-z'^ 

Consequently the differential equations (2) 


become 


X = — X j/x^-\-y^-]- 


(d + -^) 

\ i/x^ + zy 


Iz 


= ]^—dy + sj/ x^ + z^~^ ^x^ + z"^ , 


(7) 


z \ d -\- 


sy 


^ x"^ z 


— lx 


\/x^ + z^ — g. 


Again, these equations may be abbreviated as 
follows : 


- • / ^y\ 

X = — H J — Izu , 

y = u{—dy + su), 

.. . / sy\ 

z = — + — I -f Ixu — 


( 8 ) 




— . {x^ y^ z^), 'Pq obtain equation (7) , in the drag and side- 


, ways force terms was replaced by v ^ 

= y x^ + y^ z^y—dy sj/ x^ zA, (5) or by uv, but in the lift term was replaced by 

z = — z ^ + 2/^ + 2^ ( + 


sy 


^ x‘^ -\-z 


lx 


z^, or by This amounts to saying that 
D and S vary not as but as the product of v 
and its projection on the vertical plane. The 
somewhat different treatment of the lift term 


+ / . . • + 2/^ + 2:^) g- was dictated by exigencies of the differential 

yx^-hz^ 


^ CO? 


CONFIDENTIAL 


I 


EARLY STUDIES ON COLLINEARITY CONTROL 


119 


analyzer.j However it was felt that this was not 
too unrealistic for the purposes then at hand. 
In fact the lift force might certainly be de- 
creased somewhat when lateral control is also* 
applied, and such a decrease has not been other- 
wise taken into consideration. The approximate 
equations (7) reduce to (5) when Sy and hence 
2 /, is zero. 

The function initially assumed for density 
w^as 

n OC^O “2.96 X 10 "Si 

p = 0.959 Poe 

w^here po = 0.002378 slug per cubic foot is the 
density of air at sea level. Several other such 
functions were later employed, in dependence 
on the various physical circumstances which 
were relevant. There is little difference in the 
results, however, at least as far as guiding is 
concerned. 

The functions Cd, Cs, Cl were generally ob- 
tained from empirical data. Certain standard 
trajectories were obtained for the various 
bombs for full control deflections, applied, say, 
at 8, 15.5, 23, and 27 seconds after the instant 
of release. The initial velocities assumed were 
between 175 and 275 miles per hour. In general 
the initial altitude was taken as 15,000 feet, al- 
though some trajectories were obtained using 
higher and lower altitudes. 

Because of the constant modification of 
bombs and hence of coefficients, standard tra- 
jectories were also obtained for values of Cz>, 
Cl, Cs 20 per cent lower and higher than those 
in current use. From these trajectories it was 
possible by interpolation to determine the ma- 
neuverability, ranges, time of flight, trail, etc., 
of future bombs with various characteristics 
within this range. 

In another set of solutions, instead of putting 
in the values of Co and Cl corresponding to full 
deflection in range, the functions Cd and Cl were 
plotted on input tables and applied at any time 
during the course of solution and for any chosen 
deflection. 

We include here, for approximate compari- 
sons, a table of the constants of several of the 

^The machine connections of the diiferential ana- 
lyzer for the three-dimensional solutions are shown in 
Figure lA. A simpler arrangement, of course, was 
possible in the plane, when y = 0, but that was a 
special case of the connections shown. 


bomb types for which solutions were regularly 
made. 


Table 1. Tentative data on projectiles. 


Bomb 

m 

Mass 
in lb 

A 

Area 
in ft2 

S /dd 

Omax/ 

' dt 
in sec 

C/?(00) 

Min. 

Cd 

Max. 

Cl,Cs 

Max. 

RAZON A1,000 

1.865 

0.7-1. 0 

0.406 

0.978 

0.981 

AZON A 

1,000 

1.865 

0.7-1. 0 

0.265 

0.487 

0.513 

RAZON B 1,020 

1.89 

0.6 

0.262 

0.898 

0.637 

AZON B 

1,020 

1.89 

0.6 

0.262 

0.580 

0.637 

RAZON 0 2,160 

2.89 

0.6 

0.261 

0.713 

0.739 

AZONC 

2,160 

2.89 

0.6 

0.261 

0.487 

0.739 

ROC A 

1,700 

9 

1.7 

0.413 

0.673 

0.65 

ROC B 

1,700 

9 

1.7 

0.122 

0.382 

0.65 


8 3 EARLY STUDIES ON COLLINEARITY 
CONTROL 

It was generally agreed that the bomb, and 
possibly also the airplane, should for the best 
results be so maneuvered that over a finite time 
interval prior to impact the bomb, airplane, and 
target would be collinear (compare Figures 3 
and 4) . In such case all errors in dropping 
might ultimately be reduced to zero and high 
accuracy would result. It would only be neces- 
sary to provide stability in the guiding process. 
Consequently a detailed study has been made of 
this aspect of the problem, for which the use of 
the differential analyzer was invaluable. In the 
case of the RAZON bomb a point target was 
assumed, located normally where the unguided 
bomb would fall. Programmed deflections were 
applied in an attempt to arrive at a trajectory 
giving the desired collinearity during the last 
part of the flight. An ideal line of sight tra- 
jectory was constructed geometrically under 
various assumptions. For example, it was as- 
sumed that the airplane, traveling 250 miles 
per hour at the instant of release of the bomb, 
could decelerate thereafter at the rate of 2.5 
miles per hour per second. For a typical 
RAZON, the best possible trajectory that could 
be obtained from the analyzer using full posi- 
tive lift and then negative lift lay about half 
way between this ideal curve and the free-fall 
curve. 

Similar trajectories were obtained after 
shifting the target from the position of a free- 
fall hit, that is to say after allowing for either 
a rangewise or lateral offset. The lateral offset 
seemed especially attractive, since the guiding 


^ NFIDENTIAL 


120 


CONTROL OF GUIDED BOMBS 


plane would then maneuver to the opposite side 
to achieve line of sight with the bomb and 
target. 

The result of these studies has thus far been 
negative. From the trajectories calculations 
were made of where the plane would have to be 


1. The plane must be traveling during the 
last part of the flight at too low a speed. 

2. The plane must be further back than it 
might be on the assumption of a reasonable de- 
celeration. This is the most serious difficulty. 

The conclusion is that with the available 



at each second in the last part of the bomb’s 
flight in order to be collinear with bomb and 
target, assuming the target at the point where 
the bomb landed, and that the plane remained 
in horizontal flight. In each case the same two 
difficulties appeared, namely: 


bombs and airplanes, the line of sight, or col- 
linearity condition cannot be achieved without 
an undesirable maneuver. 

Some trajectories were obtained for an alti- 
tude of 28,000 feet. In these cases difficulty (1) 
did not arise. For a lateral offset of the target. 


^€®*»^P?I>ENTIAL 


COMMENTS ON EVASION BY THE BOMBER 


121 


using rudder control and evasion to the opposite 
side, the plane could travel during the last part 
of the flight at its initial velocity of 250 miles 
per hour and still be collinear with bomb and 
target. But difficulty (2) was still present; for 
line of sight the plane would have to be about 


DROP AIRPLANE 



Figure 4. Character of trajectory with CARP. 


3,000 feet back of where it would be at the given 
times for the given velocity. It may be noted 
that the necessary condition for terminal col- 
linearity, implied in (2), namely that the tan- 
gent to the trajectory at impact contain the 
observer, is also barely sufficient, in the sense 
of (1), provided of course that the bomb hits 
the target. 

The corresponding problem with lateral con- 
trol only, as in the AZON bomb, is much sim- 
pler, where a line target instead of a point 
target is assumed. Then it is a question of plane 
of sight instead of line of sight. If the bomb 
is not maneuvered and the airplane continues 
flying in the same direction as at release, then 
line target, bomb, and airplane are coplanar for 
a precise and undisturbed drop. If the airplane 
deviates from its straight course, either inad- 
vertently or deliberately as in an evasive ma- 
neuver, the bomb can be maneuvered in the 
same direction so as to achieve the plane of 
sight condition, at least terminally. The extent 
of the evasive maneuver is of course limited by 
the available maneuverability of the bomb. 
Analytic trajectories have been obtained for 


the AZON bombs using first right deflection and 
then left deflection, the change being effected at 
such a time as to make the y coordinate of the 
bomb zero at impact. This has been done for full 
rudder control to get the outer limits of the 
maneuver, and also for half deflection. In gen- 
eral it was believed that only half-control should 
be used for such evasion, leaving the rest for 
correction of dropping errors. 

To return to the most crucial matter, that of 
collinearity in the more complete sense, we 
estimated that a bomb of roughly twice the lift 
of the “standard” RAZON would be necessary 
to achieve this end. More lift than this would 
be advisable for comfortable tolerances. The 
effect of large concurrent increases in the drag 
is not as well known, but we had some indica- 
tion that this was not so important. 

» COMMENTS ON EVASION BY THE 
BOMBER 

It was considered by many of the operational 
military personnel involved that moderate eva- 
sion is very little better than none, owing to the 
dispersion of antiaircraft fire. Against fighters, 
on the other hand, effective formation tactics 
again preclude violent evasive maneuvers by 
the bomber. Furthermore, for violent evasion 
following release, the stabilizing problems and 
the visibility requirements in computing and 
sighting apparatus increase alarmingly and 
lead to very complex and novel equipment. In 
particular, this is brought about by the con- 
siderable bank of the airplane which is involved 
if a decided turn is entered into. 

An evasion may also be made for the pur- 
. pose of aiding the collinearity condition. Thus 
the use has been made of a climb to slow down 
the bomber and allow the bomb relatively to 
advance. While this may be the only way to 
obtain collinearity with a weakly maneuverable 
bomb, it is considered undesirable as a tactical 
measure. For example, if an injured bomber is 
in the formation, the other planes naturally dis- 
like to climb away from him. The latter con- 
sideration might not apply to an evasive maneu- 
ver, the term being used in both senses as above 
described, which consisted in a sustained turn 
at constant altitude (see Figure 5). It is inter- 


122 


CONTROL OF GUIDED BOMBS 



Figure 5. Special maneuver and guided trajectory. 


esting to note that such a maneuver might make 
it easier to attain collinearity of bomb and tar- 
get, and hence accuracy in both directions, to- 
ward the end of the time-of-flight. Such a tactic 
would involve dropping the bomb during a run 
on a point displaced laterally from the target 
by about one-tenth of the altitude, and entering 
on a turn to the other side just after dropping. 
A control program would turn the bomb, climb 
it, and then dive it toward the target. Manual 
control would then refine the trajectory. In such 
a process, the guiding would be made less con- 
fused due to the separation of the x and y di- 
rections which is involved in the special gyro- 
scopic method of roll stabilization already men- 
tioned. It would remain, however, in the sight- 
ing system made for this purpose, to make 
somewhat different provision (than heretofore 
considered) for separating out the influence of 
bomb motion in the z direction. 

« 5 EVOLUTION OF THE FIRST SIGHT FOR 
GUIDING 

The struggle for collinearity, in bombs of the 
type available until recently, ended in frustra- 
tion. In the design of a sight for immediate 


applicability, we were forced to accept the ear- 
lier doctrine that a guided bomb should be cor- 
rected by operations which change its trajec- 
tory but little from that in an unguided fall (see 
Figure 3). It should be emphasized that, while 
there is certainly enough maneuverability in 
such bombs to compensate for target accelera- 
tions, ballistic winds, and dropping errors, 
these facts alone cannot assure accuracy in 
range when a normal approach is made. This 
circumstance would be very different, for ex- 
ample, if the normal approach were straight 
down from vertically overhead. 

Since collinearity over an interval, as illus- 
trated, for example, in Figure 4, appeared to be 
impossible we strove for instantaneous col- 
linearity at the moment of impact. Given the 
proper guide to steer the bomb during flight, 
the range accuracy of this method depends only 
on the knowledge of flight time : and hence prin- 
cipally of bomb ballistics and altitude. It turns 
out that the properties of an instrument which 
will show how the angle between bomb and 
target should close up in time are also the prop- 
erties of the computer, if appropriately em- 
ployed, in the Norden bombsight Mark 15. This 
fact led to the attractive possibility of using 
the same group of apparatus for dropping the 
bomb and for guiding it after the drop. A dia- 
gram showing the operation of this sight is 
given in Figure 6. A normal drop is made as 
though the bomb were not to be guided. The 
operator then avoids further adjustments to the 
bombsight for synchronizing, but watches the 
target. The flare on the bomb is reflected in the 
target field in such a way as to lie directly on 
the target if the descent is proceeding accord- 
ing to plan. The desired trajectory is thus re- 
ferred to the target itself; and if the proper 
time of flight is set in, and if the operator can 
“guide” the image of the bomb always onto the 
target, he will hit. It was contemplated to use 
this method in range only, with RAZON, per- 
mitting another operator to guide in azimuth. 
The latter is thus equivalent to an AZON 
guider. If minor evasions or accelerations are 
indulged in by the bomber, this will merely 
warp the trajectory somewhat. The trajectory 
will still end in the target, if the other conditions 
are met. 


\cONFIDI^NTI.^ 


ORIGIN OF THE GUIDING SIMULATOR 


123 



IMAGE AS SEEN IN TELESCOPE, 
SHOWING CROSSHAIRS, FLARE, 
target, AND GUIDING ERRORS 


Figure 6. Mechanism for bomb images in CRAB and 

CARP. 

If, due to maneuvers either by bomber or 
target, or due to an extremely poor synchroni- 
zation by the bombardier, the target moves out 
of the field of the telescope, it is only necessary, 
and without effect on the result, to process the 
vertical gyro of the bombsight back into such a 
position that the target may again be seen. This 
should normally not be necessary, however. 

Modifications of the mechanism of CRAB, to 
lead to collinearity conditions with a more ma- 
neuverable bomb, were later developed, and 
resulted in a sight called CARP, for use with a 
flare-equipped ROC. Through the aid of this 
sight the bomb was to have been efficiently 
guided into collinearity. 

8 ^ ORIGIN OF THE GUIDING SIMULATOR 

It is analytically difficult to work successfully 
on the stability problem since (1) a human 


being is involved, as yet of unknown differential 
equation, and (2) the controls themselves are 
subject to boundary conditions in deflections 
and rates : thus making stability of the system 
between such boundaries only a necessary, and 
not a sufficient, condition for complete stability. 
As for similar problems in other fields of en- 
deavor, it was decided to use electronic simu- 
lative methods for this problem. 

Not only is it essential to be able to guide 
the bomb onto the target in angle, or onto an 
auxiliary programmed aiming point, but it 
must be possible to keep it there very closely. In 
the laboratory a reproduction of the dynamics 
involved in this operation has been developed 
and has proved to be quite useful. An account 
of the apparatus and technique of this devel- 
opment is given elsewhere. 

For the purpose of such simulation it was 
not considered necessary to duplicate in nearly 
so precise a form the overall dynamics of the 
bomb’s motion, since secondary effects, which 
follow slowly after the more immediate re- 
sponse to a guiding impulse, are of relatively 
minor importance in the control dynamics. 

By adjusting the time scale it is possible to 
include the human operator existing in con- 
junction with other elements of the causal loop, 
or to study various artificial components 
through oscillographic response to standard 
inputs. 

But the principal advantage of this approach 
is that it permits the realization, in flexible 
model form, of all the discontinuities which 
are present in the real prototype, and which 
must be dealt with in the design of auxiliary 
equipment to attain stability under all con- 
ditions and through all regions of the variables. 

A further, and not entirely accidental, prop- 
erty of this sort of simulative arrangement is 
that it may be applied as training equipment. 
Additional realism may be attained by the su- 
perposition of moving map images around the 
oscilloscope screen. It is considered that such 
application is a valuable addition to the pro- 
vision of a laboratory “proving ground” for ex- 
perimental sighting equipment. The above lab- 
oratory simulative systems, and the resulting- 
trainers, were extended later to apply to the 
ROC dynamics, having initially been built 


®NlTDENTrsir| 


124 


CONTROL OF GUIDED BOMBS 


principally around RAZON. Changes in degree, 
only, were necessary. In fact a somewhat closer 
representation was obtained owing to the aero- 
dynamic stability of the latter missile. 

« - CONDENSED SUMMARY OF CRAB AND 
CARP 

AZON and RAZON are guided bombs made 
by converting standard 1,000-pound or 2,000- 
pound bombs through replacement of the tail 
structure by a new unit containing radio, power 
supply, gyros, and fin-driving and aileron-driv- 
ing motors. They are appropriately stabilized in 
roll, and may be dropped normally and then de- 
flected moderately about a normal trajectory 
during a more or less straight continuation of 
the bomber’s run. Whereas AZON may be de- 
flected in line only, RAZON may be deflected 
both in line and in range. 

CRAB is a sight and sighting technique for 
guiding RAZON. A small mirror is attached to 
the Mark 15 telescope in such a way that the 
image of the target, which normally stays in 
the field even after the bomb is dropped, has 
superimposed on it an image of the bomb flare, 
which may then be guided onto the target. This 
results, under average conditions, in the bomb 
following a trajectory which is perfectly nor- 
mal in shape toward the end except for the 
guiding transients, and which may terminate 
in the target. CRAB may be easily installed in 
the bombsight and does not interfere with nor- 
mal bombing. With this method, it is important 
to know the bomb’s time of flight within good 
accuracy and to set in the corresponding disk 
speed. Tests from 15,000 feet gave a probable 
error of 90 feet in range and 10 feet in line. 

ROC is a somewhat different missile, still in 
development. It features a wing structure 
which permits flight with zero pitch and yaw, 
as well as a much greater maximum lift, and 
hence curvature of path. Although intended for 
other purposes, it was also developed for an 
application (remote visual guiding) much like 
that of RAZON. 

CARP, still in development, is a sight for 
ROC. It is more elaborate than CRAB, and dif- 
fers in that the angular program between the 
directions to bomb and target is not that of a 


standard (accurate) bomb. This program con- 
verges in such a way, toward the end of the 
time of flight, that the angle gradually de- 
creases to zero and remains so over an appre- 
ciable interval of time. A computer, which pro- 
duces this program and drives a mirror in an 
auxiliary telescope, derives its information 
from normal bombing data which are available 
in the bombsight, to which CARP is attached. 

Along with these sight developments, an ana- 
lytic trajectory study was carried out with the 
differential analyzer. A large library'^ of guided 
trajectories, some in three dimensions, was col- 
lected, and a complete index prepared. 

There was also the electronic simulator 
study. The purpose here was only to study the 
stability of the human guiding process. This 
has helped tremendously in the choice of guid- 
ing paraphernalia. This same technique was 
subsequently applied to the development of 
trainers for field use. 

8 « CONTROL OF RAZON FROM THE 
GROUND 

Upon a definite military request, in the sum- 
mer of 1945, cooperative conferences were ar- 
ranged among NDRC Divisions 5, 7, and 14 
(Radiation Laboratory at MIT), to study the 
question of bombing strongly held enemy posi- 
tions, such as those in caves and on hills in 
Pacific islands, from lines of advance at the 
edge of occupied territory, by remote control 
of detectable bombs dropped onto such posi- 
tions. Thus if, from two separated friendly 
points, the azimuth bearings of such a target 
were identifiable, a bomb dropping generally 
toward the target might be so guided as to fall 
on each such bearing at ground level, and con- 
sequently on the target to high precision. In 
this cooperative process, the bombing airplane 
might be appropriately guided to an appropri- 
ate dropping position by one or more of the 
ground stations. 

An early suggestion was for the application 
of such radar sets as the SCR 584 as a means 
for complete knowledge, during the drop, of the 
bomb position, and indeed for the guidance of 
the bomber. While our own studies were on the 
visual aspects of the tactic, in which the bomb 


CONTROL OF RAZON FROM THE GROUND 


125 


was to be flare-equipped and the ground sta- 
tions relatively close by, we think it appropriate 
to mention one solution, for the combined prob- 
lem of radar detection and remote guiding. It 
is assumed that the ground position is identi- 
fiable by some means and to high accuracy, in 
terms of radar coordinates, and that both 
bomber and bomb are uniquely identifiable in 
the same coordinate system. The solution was 
obtained as follows, with the SCR 584 coupled 
(say) to the M-9 antiaircraft director. Pre- 
diction would be applied in the standard man- 
ner to the bomber, as though it were a bomb, 
during the approach. That is, the future posi- 
tion of the bomb, at the end of the known time 
of flight thereof, and assuming a modified grav- 
ity acceleration after drop, would be continu- 
ously computed and indicated at every instant 
as though the bomb were dropped at that in- 
stant, by direct tracking of the bomber. Simple 
modification of the M-9 computer could accom- 
plish this, and a presentation of the potential 
ground position of the bomb would be continu- 
ously available at the single remote station. 
Thus not only could the bomber be directed into 
position, but the signal for release could be di- 
rectly provided when the predicted ground 
position of the bomb coincided with the target. 

Following release, the radar tracking would 
be switched to the falling bomb. Prediction 
would be continued, using the same future ac- 
celeration, but now with a time of flight deter- 
mined either from the remaining bomb altitude 
or the time duration since release. This would 
still provide a predicted ground intersection 
for the bomb, based on simplified, but adequate 
and continually more valid, extrapolation. Guid- 
ing would be direct and two dimensional, in 
plan. It would be relatively stable, and hence 
potentially accurate, owing to the presence of 
a first-derivative response in the prediction, 
which embodies the guiding reference. This 
method would certainly lead to very successful 
attack. Its only drawback is the weight of 
equipment required, some 17 tons, although this 
is partly compensated by the greater range 
from the control station which would be 
allowed. 

It should be noted, either with the radar or 


the visual method of control from the ground, 
that the projectile need not be dropped from a 
bomber, but could equally well be launched, 
mortarwise or by other means from the ground. 
Launching could occur from the observation 
posts or from further back. For future develop- 
ment, it seems that this freedom is significant. 

On the visual side again, probably the sim- 
plest arrangement in which control is com- 
pletely applied from the ground is that in which 
the ground stations look toward the target 
along perpendicular directions, and the bomber 
flies directly along one such direction. The roles 
of such stations could be interchanged, and 
there might be much to be gained in such sym- 
metry and flexibility. More generally, the 
bomber might attack on any track dividing the 
lines toward the target from the two ground 
stations, which indeed need not be rectangu- 
larly disposed. It is also evident that the ranges 
between stations and target need not be equal, 
and may have a large range of absolute values. 

In^ Figure 7, let A and B denote the azimuth 


BOMBER 



Figure 7. Observation scheme for ground control of 
RAZON. 


and range control stations, respectively, and T 
the target. The airplane is so directed on its ap- 
proach that its ground tack is a line GT be- 
tween AT and RT. The question of the initia- 

'The following material is adapted from an earlier 
report. 


'Suggested by G. R. Stibitz of NDRC Section 7.1. 

:ONFIDENTIAL^ 


126 


CONTROL OF GUIDED BOMBS 


tion of the drop itself will be discussed below. 

Let B be the position of the bomb at any in- 
stant, and the angle between BT and the ver- 
tical VT, The value of <j> at the instant t = 0 is 
the dropping angle <^o. Control of the bomb can 
be achieved by observation of and its projec- 
tions. Since the observer at R will see not </> 
but its projection 0 on a vertical plane perpen- 
dicular to RTy it is desirable to employ for ref- 
erence in control some function of 4> which is 
not altered by projection. 

Let xj/ be the angle GTR. Then 

tan <f)o = tan </)o sin yp. (9) 

If the bomb is so guided in azimuth as to re- 
main in the plane GTF, then 

tan 4>{t) = tan (pit) sin yp. 
Consequently 

tan (pit) _ tan (pit) 
tan 00 tan 0o 

If the bomb is allowed to deviate somewhat 
from the plane GTV, this relation will not hold 
exactly, but in general such deviations will be 
slight, and will not affect the guiding process. 

The function tan 0(t)/tan <Po is also un- 
altered by variation of the airspeed of the 
bombing plane. A difference of 75 miles per 
hour in velocity produces less than 1 per cent 
change in tan (t)/tan 0o, this change being 
due to the increase in the horizontal component 
of drag at higher speeds. 

It follows that tan 0/tan <po is a function of 
time and initial altitude only: 


( 10 ) 

( 11 ) 


a cam driven at a rate dependent on altitude. 
If the bombsight Mark 15 should be used for 
tracking, the function kih) is not necessary. 
The cam for fit,h) may be driven by the con- 
stant speed motor through the disk whose speed 
is inversely proportional to the time of flight 
of the bomb. 

The functions fit, 15,000) and kih) may be 
readily calculated from free-fall trajectories 
run on the differential analyzer. The bomb 
should be guided around the free-fall case. One 
operator might track the bomb with the cross 
hair, making such adjustments to the telescope 
as may be necessary to keep the bomb on the 
cross hair and in the field of view. A second 
operator might then control the bomb. From 
the telescope position the actual value of 
tan 0'(t) is obtained and the ratio tan 0'(t)/ 
tan 00 is formed. The primes are used to dis- 
tinguish observed values from theoretical ones. 
This ratio is to be compared at each instant 
with the values given by fit,h). For a perfect 
drop 


tan 0'(O 1 

tan 0o' fit, h) 


(16) 


tan (p'it) 
fit, h) 


— tan 00 = 0. 


(17) 


However it is not necessary, or even desirable, 
that the bomb be controlled so as to keep the 
right-hand side of equation (17) zero. A crite- 
rion for a hit is that tan 0 remain finite. Hence 
it is sufficient to keep this quantity approxi- 
mately constant. 


tan ^ 

- fit,}l). 

tan 00 

(12) 

The variation with altitude may be handled by 
stretching of the time scale. If 15,000 feet is 
taken as standard altitude, then 

15,000), 

where 

(13) 

o 

??- 

II 

(14) 

15,000). 

(15) 

Consequently only one function of 

time, fit, 


15,000) , is needed. This could be mechanized by 


tan (p' fit) 

fit,h) 


— / 

tan 00 


= C. 


(18) 


The value of C may be indicated by a pointer 
on a scale (having many divisions, and also 
perhaps a special pattern) whose center point 
corresponds to zero. The operator would guide 
the bomb in such a way as to keep the needle 
as stationary as possible. The initial value of C 
Sit t = 0 would be approximately zero. During 
the drop the needle might deviate from the cen- 
tral position for a variety of reasons, but it 
should not be necessary to control the bomb so 
as to make the needle return to that or any 
other given position. A change in actual drag 


»fd^NFIDENTIAIj^: 


CONTROL OF RAZON FROM THE GROUND 


127 


coefficient Cd from the value used in calculating 
f(t,h) may cause C to vary slightly. Change in 
time of flight due to application of control 'will 
cause small variation in C. Deviation of the 
bomb from the vertical plane GTV may also 
alter the perspective relationship and hence C. 
But all these effects are slight and would cause 
practically imperceptible motion of the needle. 

An error in dropping, however, where the 
bomb, if unguided, would miss the target, would 
sooner or later cause a quite perceptible change 
in C, increasing with time, since tan ^ in such 
a case becomes infinite at impact. In the case 
of a prospective miss of 100 feet short on the 
ground for v = 250 miles per hour and x}/ = 90 
degrees, C will increase at the rate of 15 per 
cent per second 9 or 10 seconds before impact, 
this rate rapidly increasing with time. The 
same statement holds for a 100-foot overshoot, 
except that C is decreasing in that case. This 
allows ample time for correction of the error. 
For a larger error on the ground a 15 per cent 
per second change in C would occur somewhat 
earlier in flight. The value of C at any time is 
nearly proportional to the prospective error, 
provided C is changing with time. 

It is desirable that both stations A and R be 
similarly equipped and operated, so as to be 
readily interchangeable in function. Hence it is 
recommended that azimuth control be exactly 
like range control, basically recognizing the 
same angle <f>. Station A will observe the pro- 
jection of on a vertical plane perpendicular to 
AT. If the bomber flies so that its ground track 
lies along AT, the tangent of the projected 
dropping angle is zero, but the method of range 
control is still applicable to azimuth. 

It is possible for the airplane to drop the 
bomb as usual with its bombsight. However, it 
might be desirable to direct the release from 
one of the ground stations, say R. R could track 
the airplane prior to release with the same 
mechanism to be used later for the bomb. The 
usual release condition could be used : 


plane and perpendicular to RT. Consequently 
his release condition becomes 


Vctf 

tan 00 = — T, 

h 


( 19 ) 


. — '^ctf . . 

tan 00 = T sin 0, 

h 


( 20 ) 


where r is angular trail in mils. However, the 
operator at R would observe these quantities 
projected on a vertical plane through the air- 


where Vc is the projection of Vc» If the syn- 
chronous sight is used, Vc/h would be syn- 
chronized just as Vc/h is in the normal pro- 
cedure. The only difficulty is the projection 
of the trail r. This is the only part of the whole 
process where a knowledge of the angle 0 is 
needed. If the airplane is guided over the line 
AT, then 0 is readily determined by measure- 
ment of the angles ART and RAT, as shown in 
Figure 7. 

A mechanism for embodiment of somewhat 
the same principle as above described has been 
planned.™ Development along such lines may 
continue, beyond termination of contractual 
relations between that organization and NDRC 
Division 5, under the auspices of the special 
weapons branch of ATSC at Wright Field. 

An interesting rationalization which bears on 
this problem is based on vacuum flight condi- 
tions for the bomb and relates to behavior of 
the angle 0 as above employed. Consider a per- 
fect unguided drop. Whereas before release the 
rate of change of tan 0 was uniform, after re- 
lease the rate of change of cot <f> will be uni- 
form. We refer, of course, to the bomb itself in 
both cases. In fact 


Before release: — tan 4>=- 
dt h 


d 


9 


After release: — cot (b = ^ 
dt 2v 


( 21 ) 

( 22 ) 


where v is the horizontal component of the 
bomb’s velocity, in target coordinates, or the 
closing speed of the bomber. 

It has been proposed that this property be 
used in ground control of RAZONs, guiding the 
bomb in such a way as to hold d cot (f>/dt con- 
stant. Such control would cause little deviation 
from a free-fall trajectory and would insure a 
hit. It is evident that during both regimes, be- 
fore and after release, a simple mechanism 
would suffice for tracking or for the guiding 
criterion, being based on the above equation. 

*"By H. A. Van Dyke, of L. H. Schwien Engineering 
Company, in consultations with the writer. 



128 


CONTROL OF GUIDED BOMBS 


Horizontal and vertical “tangent-screws,” for 
example, might here be involved. It might fur- 
ther be desirable to use the cotangent criterion 
in directing from the ground the release of the 
bomb. 

Let a Cartesian coordinate system be set up 
with origin at the target T, and x axis along the 
ground track of the bombing airplane (cf. 
earlier sections and figures of this chapter). 
Let" P be the position of the airplane at any 
instant before release, h its altitude, v its 
ground speed. The ground station directing re- 
lease is at R, RT making the angle ij/ with the 
X axis, as before. 

Let bars denote projections on a vertical 
plane perpendicular to RT; for example, <f> is 
the projected value of (f> as observed at the 
station R. Then 

cot 0 = cot <f) CSC \p, (23) 

and 

CSC (24) 

dt I dt 

For a nonvacuum bomb at the instant of 
release 


d cot </) _ /(Cp) 
dt V 


(25) 


instead of the condition given by equation ( 22 ) . 
Here fiCn) depends only on the drag coefficient 
Cd, and has the dimensions length/time% In 
particular f(0)= g/2. By equations (24) and 
(25), at the release point, 

d cot 0 ^ fiCp) _ fjCp) ^ 20 ) 

dt V sin xj/ V 
We also know that 


_ h 
cot 0 = — , 

X 

and consequently 

d cot ^ h 

since certainly dx/dt = — v. 
Consequently we obtain the simple new 
criterion 


(27) 

(28) 

release 


l_dcotcf> _ IfiC^^ 
cot (t> dt \ h ’ 

Thus the whole operation might be carried out 

"The present exposition is based on a study by 
R. M. Peters of Section 7.2. 


in terms of the cotangent, and the fact may 
have broader significance yet for bombing. 

We note that in vacuo we have simply, as a 
release condition, 

cot <t> dt tf 

8 ^ CONTROLS FOR THE TELEVISION BOMB 

We have described earlier in this chapter 
the general arrangement for television guiding, 
as of ROC, where a remote operator tracks 
the departure of the target, given say by the 
variable “lead” A, on the screen and thereby, 
through established control dynamics, affects 
the corresponding deflection 8 of the appropri- 
ate control surface of the projectile. The mo- 
tion /X of a tracking handle which he manipu- 
lates in this process can be conducted both to A 
and to 8 , so that merely by holding an ihdex 
on the target, the operator automatically main- 
tains a relationship between A and 8, by virtue 
of the dynamic connections involved. A major 
question is where to include the control dy- 
namics, whether between ix and A or between 
/X and 8. Apparently either procedure is valid, 
being respectively analogous to that for a lead- 
computing sight (so-called) and a director, in 
more orthodox fields. We shall here avoid this 
question by considering only the result, which 
is embodied in the effective dynamic relation 
to be established between A and 8, in each 
coordinate. 

In Chapter 1 we have spoken of the various 
means for attaining a collision or interception 
course for a vehicle with respect to a target. 
Here it was not considered possible to install 
new gyro equipment in the bomb, but by a 
peculiar stratagem, mentioned elsewhere from 
the philosophical standpoint, and exposed in 
more detail below, it was found possible to ob- 
tain equivalent dynamics without additional 
equipment in the bomb. 

The characteristic equations herein proposed 
were first tested on an electronic simulative 
structure, referred to briefly in Chapter 4 on 
simulation, in which the human operator could 
be involved. Stable subsidence to an intercep- 
tion approach was found to occur, without 
critical adjustments being necessary in the 


f ^onfidentiaD 


CONTROLS FOR THE TELEVISION BOMB 


129 


auxiliary regulatory controls. This conclusion 
was later checked by model studies on a larger 
scale, thus continuing the verification of the 
electronic model technique in exploratory roles. 

In the following analysis we refer to Figure 
8, showing the bomb falling in the air mass 
toward the target. 

It is assumed initially that the bomb has no 
attack angle, so that the longitudinal axis of 


where is a constant greater than one, and to 
is a constant angular rate. An important special 
case, incidentally, occurs when to = 0. Since 

T = 0+X, (33) 

equation (32) gives 

0 = j^^X + a.. (34) 


\ 

\ 

\ 


\ 

\ 




Figure 8. Range problem for television bomb. 


the missile is in the direction of its velocity 
vector. The velocity of the target is Vey and that 
of the projectile is v^, both such velocities being 
measured with respect to the air mass. Then 
from the figure, assuming X small (cf. Chap- 
ter 1), 


• V-pX . VeCOS<f> 


(31) 


Suppose control is applied to the bomb in such 
a way as to make it turn in the air according to 


Eliminating in equation (31) by use of equa- 
tion (34) 



VpX 

ir + 


Ve COS 0 


CO . 


Now since, approximately. 


(35) 


'dt~ 

equation (35) may be written as a differential 
equation in A and R : 


dX=-dffi + -i(x - dR . (37) 

N — 1 Vp R\ Vp J 

Let 

T] = cos (f ) , (38) 

Vp 

and 


X* = X - ry . (39) 

Then equation (37) becomes 



If Vp and r) are assumed to be constant, equation 
(40) is a homogenous differential equation in 
A* and R whose solution for the case A 4= 2 is 


N — 2 o)Ro 
^ N-l'^ VpXo* 

V ~ \^/ N -2 coi? ' 
N-l'^ t>pX* 


(41) 

(^4=1,2) 


where Ao* and Rq are initial values of the vari- 
ables. In the special case N = 2, the solution is 


R ^ 0) R 

X* = ~ Xo* + ~ In ’ 
JXiQ Vp JXq 


iN=2) 


(42) 


N 

N- 1 


*X + CO , 


(32) 


In both cases A* 0 as 0. That is, the lead 
7 ), the proper value for a collision course. 


^,onfidential|^ 


130 


CONTROL OF GUIDED BOMBS 


If (o is zero, equation (41) becomes 



The next question is how to control the bomb 
so as to satisfy equation (32). The acceleration 
normal to the path of the bomb is 

Vvl = - — gsiny, (44) 

TTl 

where L is the lift force acting on the bomb as 
the result of control : 


(45) 

Here p is the air density, A is the area of the 
wing or control surface, 8 is angle of incidence 
of the wing. Define 


i pv pA 'iC L 

Ty 2m dd 


Then 


1 g . 






Or 

8 

■ , g ■ 

y H sin y . 

(47) 


'Ty ~ 

Vp 



From equation (32) and the equation obtained 
from it by integration. 


7 = ^ (X “ Xo) + CO (< — to) + To ; (48) 

it follows that 
8 N • 

Ty~ 

+ ^ sin jjy _ (X — Xo) + 0 ) (< — to) + 7o| 

N . 

" AT- 1 ^ + " 


CO (^ — to) + 7o 

+ ^ sin jco (t — to) + Toj . 

This is the equation governing the control of the 
bomb, where Vp and Ty are to be given as func- 
tions of t, while X and A are to be obtained from 
the television screen. The initial values Ao and yo 
can be most easily determined at some instant 
before control is applied, in which case yo can 
be obtained from the function y = y{t) for a 
free fall. All these functions of time will depend 




N 


VpN — I 


(X — Xo) cos 


on the velocity of the airplane at the instant of 
release of the bomb. 

In case the target has a component of velocity 
in azimuth, the same development holds in that 
direction as for elevation, except that all terms in 
g disappear and the control equation becomes 
simply 

8 N . 

y^-jy^-lX + W, (50) 

where S is rudder instead of elevator angle, and 
A is the azimuth component of lead. This separa- 
tion of azimuth and elevation lead and control 
is valid when the bomb is roll-stabilized. 

It may happen that the bomb has an attack 
angle a due to a slight shift in the center of 
gravity, which, neglecting transients, is given 
approximately by 

a = uCl- (51) 

The factor a is positive if the center of gravity 
is aft of the position for zero attack angle. Then 
the lead observed on the scope and supplied to 
equation (49) or rather to a mechanism embody- 
ing this characteristic, is not the actual lead 
A but a value A' including tz : 


X' = X + a . (52) 

The quantity is also altered by the pres- 

ence of an attack angle. If the new value is 
denoted by dC//d8 then® 

d8 1 - 3.43a d8 

for 8 and a measured in radians. Equation (51) 
may be written 

JCl' , 


a = a- —— 8 . 
d8 


(54) 


Replacing A by A' in equation (49) gives 

1 g N dCL' r 

— -a ——cos «(< - <o) + TO 5 

Ty Vp N — 1 d8 L J 


N - dCi' . 

■ a 8 

N - 1 d8 


N 


N- 1 


< ^ 0 N 

X + CO — 7 (X — Xo) COS 


VpN — 1 


l^co {t — to) + Xo J 
+ — sin j^co {t — to) + To J • (55) 


It has been assumed that 8o is zero. 


“This function was furnished by W. B. Klemperer 
of the Douglas Aircraft Co. 


'onfh)p:ntial 


SINEAD’S PARADOX 


131 


Equation (55) is not altered in form by the 
presence of an attack angle, except for the 
change in Ty due to the change in dCL/dS. 

For the ROC projectile, currently (1944-45), 

1 _ 0.244pyp 
Ty ~ 1- 3.43a 

and 

dCl _ 2.85 

d8 ~ ~ 1 - 3.43a 

with 

I 5 I ^ 0.227 radians, | a | ^ 0.0506 (approx.). 

The quantities p and Vp are functions of time 
which will depend on the initial altitude and 
velocity, and also on the control applied to the 
bomb. They have been computed approximately 
from differential analyzer data for ROC with 
full brakes (Cd = 0.413 for no control), initial 
altitude 15,000 feet, initial velocity 250 miles 
per hour, assuming a moderate amount of con- 
trol and a time of flight of 40 seconds. These 
variable parameters are tabulated against the 
duration of the drop in Table 2. The angle yo at 
time to is to be determined from the function 
y(t) computed for a free fall. 

« 10 SINEAD’S PARADOX 

In connection with dynamic means whereby 
an interception course can be stably attained by 
a homing missile, there is currently a good deal 
of misunderstanding.p Since gyro equipment 
could not be added to the bomb, it was difficult 
to see how one might use the means^ of propor- 
tional navigation, as described in Chapter 1, 
wherein one made the vehicle turn in the medium 
n times as fast as did the line of sight. In the 

‘’For the particular case of ROC-MIMO, which 
nevertheless has definite and general significances, the 
present writer dealt, on this whole question, at some 
length and very pleasurably with W. B. Klemperer 
of Douglas Aircraft. The latter organization had the 
ROC projectile, in its various phases, under direct de- 
velopment. WBK had been working for some time 
past on the problem of guiding and seeking, and had 
disseminated much knowledge and many original 
theoretical and practical structures for attack upon 
the problem. 

^The reader should compare, for example, the re- 
port: Some Aspects of the Design of Homing Aero- 
Missiles, by H. L. Dryden, to Division 5 from National 
Bureau of Standards. 


Table 2. Estimated functions for the ROC-MIMO 
projectile. 

h = 15,000 feet 
V = 250 mi/hr = 366.7 ft/sec 


i(sec) 

p (slugs /ft3) 

yp(ft/sec) 

7o(free fall) 
(degrees) 

0 

.001460 

367 

90.00 

1 

.001462 

361 

84.95 

2 

.001465 

359 

79.87 

3 

.001470 

359 

74.86 

4 

.001476 

362 

69.97 

5 

.001483 

367 

65.30 

6 

.001490 

375 

60.87 

7 

.001500 

384 

56.71 

8 

.001510 

394 

52.83 

9 

.001520 

406 

49.25 

10 

.001530 

414 

45.95 

11 

.001540 

426 

42.92 

12 

.001550 

436 

40.13 

13 

.001570 

446 

37.57 

14 

.001585 

457 

35.22 

15 

.001605 

467 

33.06 

16 

.001625 

477 

31.10 

17 

.001645 

487 

29.26 

18 

.001665 

496 

27.59 

19 

.001685 

505 

25.90 

20 

.001710 

514 

24.56 

21 

.001730 

522 

23.20 

22 

.001755 

530 

21.95 

23 

.001775 

538 

20.77 

24 

.001800 

545 

19.68 

25 

.001827 

553 

18.66 

26 

.001855 

559 

17.17 

27 

.001885 

565 

16.79 

28 

.001910 

571 

15.94 

29 

.001938 

576 

15.13 

30 

.001970 

581 

14.35 

31 

.001997 

585 

13.66 

32 

.002026 

589 

12.95 

33 

.002060 

593 

12.33 

34 

.002090 

595 

11.72 

35 

.002120 

597 

11.14 

36 

.002150 

598 

10.59 

37 

.002185 

599 


38 

.002215 

600 


39 

.002245 

600 


40 

.002280 

600 



projection shown in Figure 8, for example, this 
desirable criterion would amount, in a special 
case, to 

7 = . (56) 

Our proposal for attaining equivalent, although 
somewhat generalized dynamics, as described 
above, was to make 

7 = X (n > 1) , (57) 

this being equivalent to equation (56), since 


ONPlpSXTfSrr 


7 


132 


CONTROL OF GUIDED BOMBS 


identically and by definition 

y = X -j- 0 . (58) 

Consider the significance, stepwise, of equa- 
tion (57) as it stands, as a guiding criterion. 
In terms of finite alterations, we have 

Ay = NA\ , (59) 

where A/' is a positive numerical quantity. Con- 
sidering this criterion in terms of Figure 8, for 
example, assume that during the approach the 
target were to slow down, so that A increased. 
It is evident that to reattain, or to come further 
toward, a collision course, the bomb must now 
be more steeply dived. But what does equation 
(59) instruct us to do? It appears to indicate 
an increase in y, giving a shallower dive. 
Evidently this manner of control is unstable. 
And the instability seems permanent. There is, 
however, a paradox here, which gave rise to 
protracted arguments, in the writer’s case, and 
which deserves the title of the present section. 
Paradoxically, this criterion is perfectly stable, 
as developed in the previous section. The trouble 
is with our logic. In the first place, the stepwise 
argument, as given, is invalid — since it ignores 
equation (58). It is evident, further, that equa- 
tion (57) is completely equivalent to (56), it- 
self corresponding to known mechanisms, as 
shown, for example, by the inset in Figure 8. 
Generalizations to space are immediate, though 
not trivial, when the manner of roll-stabiliza- 
tion is specified. 

Note that in general y, in two components, 
may be provided by absolute angular rate 
meters (see Chapter 3) installed in the projec- 
tile, whereas A is available from the local detec- 
tion of relative target direction. Thus equation 
(57) may be directly mechanized, whereas ex- 
plicitly equation (56) would require local free- 
gyro references. We have assumed, in this sim- 
plified exposition, that pitch and yaw, relative 
to the medium, are zero. Otherwise a more in- 
volved analysis, as earlier outlined, is required. 
Finally, we remark that in MIMO-ROC, the 
effect of proportional navigation, using the term 
as here generalized and liberalized, was attained 
experimentally with no additional equipment in 
the projectile. 


« GUIDED ROCKETS AND THE FUTURE 

The writer will here permit himself a few 
brief remarks in a field not otherwise dealt 
with in this report, which however treats both 
of rockets and guided bombs. 

It appears that there are several lessons 
which should be perpetuated in that broader 
field. One is that there is no substitute for the 
collision course, or at least for courses lying 
much nearer to the collision, or interception 
type than to the pursuit type. We refer here 
exclusively to guidance from the vantage point 
of the projectile, rather than the remote method, 
for example by collinearity, which tends to in- 
terception, anyhow, at infinite observing range. 
Another lesson is that by proper control dynam- 
ics, giving subsidence in agreement with exist- 
ing theory to intercepting conditions, the case 
of a target moving in the medium reduces essen- 
tially to that of a target stationary therein. 

We add a few further opinions. (1) Absolute 
angular rate meters, of high sensitivity and 
performance, will probably replace free gyros 
for control references, owing to their lack of 
limits and to the compactness to which they 
may be reduced practically. (2) Ambitious 
projects in guided missiles, where complex con- 
trols and interlocks are involved, will be greatly 
advanced through the extensive application of 
the methods of electronic simulation, in the 
study stage, for the determination of param- 
eters for stability. Owing to the inherent and 
sometimes hidden nonlinearities of such sys- 
tems, analytic methods are almost utterly im- 
potent there except for certain necessary con- 
ditions under control circumstances. Through 
such models or simulators, however, nonlinear- 
ities may be readily and naturally recognized, 
and speculative dynamic components may be 
proved or disproved or altered at a moment’s 
notice. Rocket propulsion should hold no ana- 
lytic terrors for simulators, and aerodynamic 
data may be directly incorporated, once deter- 
mined, by independent testing of components 
and reduced, say, to graphical form. We note 
in passing the appropriateness of the ROC type 
of projectile for this purpose. 



Chapter 9 


AIMING OF ROCKETS FROM AIRPLANES 


9 1 SUMMARY OF PROJECTS AND WORK 

W HEN THE 3."5 FORWARD-FIRED aircraft rocket 
[AR] came into prominence as an anti- 
submarine measure in naval operations, it was 
natural, since we had already dealt with air- 
borne aiming controls for antisubmarine bomb- 
ing and were fairly well saturated with the 
larger problems of this type of warfare, that we 
became involved in the development of rocket 
sights for this application. Apparently the ques- 
tion of a sight for rockets had been given at- 
tention, during the earlier development of that 
missile, only by a few, although it is understood 
that requests for liaison had been made by 
fire control groups in NDRC before the writer’s 
engagement in 1942. In any case no such sights 
were available, except reflecting sights with 
fixed settings, and no development projects were 
in process for aiming controls when our rocket 
activities began in 1943. At least this was the 
case to the best of the writer’s knowledge and 
information. 

We were approached, in November of 1943,*'^ 
with a request to construct a computing sight 
for the aiming of rockets against sea targets: 
chiefly German submarines. At that time it was 
principally the 3."5 AR, as already mentioned, 
with solid head, with the old JP propellant, and 
launched from the now obsolescent rails, that 
was used, but even this weapon, patterned 
somewhat after the corresponding British RP, 
and later to be vastly improved, was appropri- 
ate, owing partly to its excellent underwater 
trajectory and partly to the deteriorating effect 
it had on enemy morale, as an antisubmarine 
measure at a time when the menace was still 
growing. The airplanes in which we were then 
concerned with installations were the Ventura 
and the Avenger, and the aiming was to be car- 
ried out by the pilot, substantially alone. We 
had used the radio altimeter, prior to this time, 
for automatic setting of aiming computers, and 

“By Commander G. R. Fiss of the Antisubmarine 
Development Detachment at NAS Quonset, under Cap- 
tain A. B. Vosseller. 


it was suggested*^ that this instrument be made 
the basis for a rocket sight. With a fast and 
consistent measurement of altitude over the 
water, and a reasonably good measurement or 
estimation of the glide angle toward the target, 
a computation of the trajectory, and hence of 
the superelevation allowance for gravity drop, 
could be continuously made. This represented 
an approximation, of course, even aside from 
the kinematical correction for target motion 
in the air mass and the aerodynamics of launch- 
ing, since airspeed and temperature should 
also be accounted for. However, on the basis 
of the meager information then available on the 
projectile, a computing system was blocked out 
and an experimental model was flown in less 
than two months from the original request. The 
results were irregular but promising. 

Better information was soon acquired on the 
behavior of the rocket, partly by visits of the 
writer and others to California Institute of 
Technology [CIT] in Pasadena, and a develop- 
ment program for a sight (originally this proj- 
ect, and its initial product, was called VERB), 
later called RASP, was arranged at a consider- 
able level of priority. A special deflectable sight 
head was prepared, from a “retiflector” which 
had fixed optics, by moving the normally sta- 
tionary reticle in two dimensions by remotely 
controlled d-c servos. It was thus possible to 
deflect the line of sight, for automatic aiming, 
by voltages developed for azimuthal and eleva- 
tional corrections in a computer placed else- 
where. Inputs to the computer included auto- 
matic radio altitude, automatic glide from a 
special gyro horizon, airspeed in either manual 
or automatic form, temperature, and a vecto- 
rially computed measurement of the target 
speed in the air mass. The computation was in 
terms of sums of products of functions of these 
inputs, and was determined on a semi-empirical 
basis. Attenuators in a-c circuits were physi- 
cally applied for this purpose, fed by servos 
and autosyn transmission for the automatic 

•"By Commander Fiss. 


•ONFIDENTIAL 


I 


133 


134 


AIMING OF ROCKETS FROM AIRPLANES 


inputs. Three distinct developmental models 
were prepared, each being tested at some length 
both in the laboratory and in the air. Accuracy 
of fire, roughly independent of range up to 
2,000 yards, improved until dispersions of 
about 5 to 7 mils were experienced regularly. 
Each model of RASP was progressively more 
compact and easier to operate. Request for 
large-scale production was made by the Atlantic 
Fleet, but before the machinery for this was 
arranged the urgency had decreased to a far 
more comfortable degree for all concerned. 

While the RASP development was still in 
progress, a separate development was begun 
under our auspices, principally carried on 
at The Franklin Institute, and now recognized 
under Navy Project NO-216 for rocket-sight re- 
search, which aimed at a major simplification 
of the computing and aiming system. By this 
time it was desired also to instrument single- 
seater airplanes, mostly fighters, for effective 
rocket fire. The problems here differed con- 
siderably, and for several reasons. For one 
thing the tactics were far more violent, so that 
certain components, such as gyro horizons in 
available form, could not be used for automatic 
inputs. Similarly, much steeper glides were pos- 
sible, and the computation in this region was 
different, requiring other instrument technique. 
The problem of space was far more stringent, 
and in particular only highly specialized sight- 
ing equipment could be put before the pilot. In 
this connection, the availability of the Marks 
21 and 23 gyro gunsights, and later the Army 
K-15, was to be taken advantage of for the new 
project, which acquired the somewhat ludicrous 
name of GRASP. Such sights'" as the gunsight 
Mark 21 provided, for GRASP, only the means 
for deflecting a line of sight developed by a sep- 
arate computer. The basic idea for GRASP,*^ was 

'Actually, they were not used operationally by the 
Navy to any considerable extent, whereas the Army 
sight, derived from the Navy prototypes, saw a good 
deal of combat action. For RASP, the Mark 1 sight 
unit, which adapted the gunsight Mark 8 to automatic 
elevational deflection, was later employed in experi- 
mental models, and subsequently this sight unit be- 
came available in Navy fighters, so that it might thus 
have been used for GRASP. Several paradoxes are 
contained in these circumstances, which were, never- 
theless, unpredictable to us during development. 

‘’Proposed by E. C. Cooper to the writer at The 
Franklin Institute. 


to compute, during a direct gliding attack, the 
altitude at which a given range would be at- 
tained from the target, applying for this pur- 
pose a measurement of the glide angle : actually 
obtained from the “vertical” component of 
gravity, properly interpreted and presented. 
The range itself, at and beyond this critical 
range, or continuously as the attack progressed, 
was to be indicated in terms of the airspeed 
and time approximately as the definite integral 
of the range rate added (note the sign) to the 
critical range. Then with range, glide angle, 
airspeed, and temperature as inputs, an auto- 
matic computation of the gravity-drop and 
aerodynamic connections w^ould be made and 
applied to the sight head. Thus the pilot, on the 
approach, merely noted when his altimeter 
agreed with the indication of the critical-alti- 
tude display, pushed a button, and aimed by 
tracking the target in his automatically de- 
flected sight. Kinematic lead was not computed, 
although an accidental correction entered for 
part of this error, and it was planned ulti- 
mately, if it proved essential, to use the lead- 
computing properties of the gyro gunsight be- 
ing employed as a deflected sight head. We note 
that an advantage of the GRASP proposal for 
fighters which carried rockets and alternatively 
fulfilled their normal function, was that a rapid 
change-over was possible from gunnery aiming 
to rocketry aiming, since the same basic sight 
was employed for both, only electrical switch- 
ing being necessary for the adaptation. This 
circumstance is of interest in connection with 
the PUSS project, discussed in Chapter 10, on 
integrated controls. A very elaborate program 
of testing was conducted on the GRASP equip- 
ment, which became extremely compact and 
progressively simpler to use. Tests ranged from 
laboratory procedures through flight tests of 
components, to full-scale firing tests at NOTS, 
Inyokern. A very high accuracy was finally at- 
tained, relative both to the dispersion of the 
weapon and to competitive equipment, of which 
latter there came to be many examples. V-J day 
terminated the latest tests abruptly, and it is 
unknown whether continuation of this project, 
principally an interim development, will be con- 
sidered to be as warranted. The second model 
of GRASP became aircraft rocket sight Mark 2. 


NATURE OF THE WEAPON 


135 


A smaller project was that for development 
of the miniature rocket sight known as PARS. 
This project was initiated at The Franklin In- 
stitute.® Inputs were motion of a damped and 
spring-restrained mass (to measure the vertical 
acceleration), deflections of capsule diaphragms 
for barometric altitude and indicated airspeed, 
the temperature being manually set in. Small 
linkage resolved these inputs and yielded a me- 
chanical motion as output, measuring the total 
allowance in elevation, which was both indicated 
on a scale for visual reference and servo-dupli- 
cated at the sight head. Although flight tests 
were carried out, of models of this instrument, 
and considerable Service interest was in evi- 
dence, no time was available finally for definitive 
firing tests. The equipment called PARS was 
designated Aircraft Rocket Sight Mark 3, and 
also Computer Mark 36, by BuOrd. This very in- 
teresting development, which was supported 
partly to test a computational method for em- 
ployment in more ambitious projects (see for 
example, in this connection, PUSS) will prob- 
ably be reported on in more detail by those men^ 
who cooperated in the theory and design. 

Finally, the PUSS project itself, for the de- 
velopment of integrated aiming controls for 
the usage of pilots, contained a computation 
for rocketry as its central solution and reason 
for being. While this project is treated else- 
where, we point out here that the rocketry so- 
lution was considered the most complex of the 
problems to be solved by this equipment, and 
the apparatus for that solution was most read- 
ily adaptable to the companion problems of 
gunnery and bombing which were to be in- 
cluded as capabilities of the system. Briefly, a 
new angular rate method was developed, for 
computation of both gravity correction and 
kinematic lead. The inputs were : angular rates 
in space of the thrust axis of the airplane, air- 
speed, altitude, and glide angle. Although the 
several variants of the method admitted dif- 
ferent sets of input data, as with radar range 

*By the cooperative promotion of H. Whitney of 
AMG-C and the present writer, following a proposal 
by the former for a compact all-mechanical computer 
to solve for the gravity, aerodynamic, and (partially 
and approximately) the kinematic corrections, for air- 
borne rockets. 

Whitney and others of AMG-C. 


explicitly provided, the method as such was 
characterized by relative insensitivity to the 
“classical” inputs, including the range itself, 
being more heavily dependent on the measure- 
ment (or provision) of absolute angular rates 
for its ultimate accuracy of aim. The measure- 
ments of such quantities are elsewhere discussed, 
and we note only that a major question is what 
particular method, among those experimentally 
available, should be exploited. The technique of 
rocketry proposed for PUSS is somewhat anal- 
ogous, although far more general in capability 
and concept, to several other methods which 
have arisen in different quarters. Thus the 
fundamental property whereby a lead diminish- 
ing with range is generatable by means of a 
downward-rotating line of sight, measured in 
space, is characteristic of certain independent 
proposals by the writer.^ 

9 2 NATURE OF THE WEAPON 

The forward-fired, finned, aircraft rocket, 
exemplified by the Navy 5."0 HVAR for ex- 
ample, has many attractions as a tactical 
weapon, particularly for lighter offensive air- 
planes such as those of the carrier-borne variety. 
Its characteristics relevant to such application 
include: the penetration and explosive power 
delivered in comparison with the weight of 
firing equipment and in comparison with the 
shock of projection; the small dispersion, or 
unpredictability of trajectory, which for- 
tunately becomes still smaller as the launching 
speed increases; and the proved effect on the 
morale of the attacked. We speak principally 
of targets at ground level. 

In leaving the airplane, the rocket-round ac- 
celerates along its trajectory at something like 
50 times gravity for just about a second, 
during burning of the propellant, after which 
it has attained a total airspeed of about 1,500 
feet per second and subsequently flies somewhat 
as a standard unpropelled projectile. In its 

^Original although not necessarily novel in a more 
comprehensive history of the Draper/Davis method 
of glide bombing, of E. P. Cooper’s proposal for a 
rocket sight in which an additive deflection is given 
to a gyro gunsight employed with a long characteristic 
time, and of the somewhat similar British method, so 
called, for rocket Are with the gyro gunsight. 


136 


AIMING OF ROCKETS FROM AIRPLANES 


initial phase of flight following the launching, 
the round necessarily follows an air path rather 
close to that of the airplane, since its accumu- 
lated relative speed is small. Being flnned, it is 
erected in the air stream and subsequently is 
urged on by its propellant substantially in this 
same direction, which is thus more nearly that 
of the flight path of the airplane — at launching 
— than that of the initial heading, either of 
the round or of the airplane. Thus the rocket 
behaves more like a fast bomb than like a 
bullet or shell, and this fact is of primary im- 
portance in the matter of aiming. 

During flight, the shape of the air path is 
somewhat different from that of either a bomb 
or bullet, although it lies approximately half- 
way between, all three projectiles being as- 
sumed released at the same speed and glide. A 
special type of trajectory is followed during 
the first 500 yards or so of flight through the 
air, that is to say during burning, which is 
characterized by an oscillation of small ampli- 
tude and a space period of some 100 yards, and 
in which the trajectory is bent downward more 
than in the immediate period following burn- 
ing. For most purposes a rather satisfactory 
analogy may be used between the rocket trajec- 
tory and that of more orthodox projectiles, even 
in vacuo. Thus a good approximation is af- 
forded by fitting parabolas to the trajectories 
of these rounds, corresponding in a variety of 
ways to equivalent trajectories in vacuo. For 
example, it suffices, to good accuracy, to say that 
the round behaves like a projectile fired in 
vacuo along a parallel path which originates 
behind and above the actual firing position, and 
at a different initial velocity, which incidentally 
must be a function at least of airspeed and tem- 
perature. Again it has been found that the 
rocket trajectory may be replaced by a para- 
bolic path corresponding to that of a hypotheti- 
cal projectile launched at a definable angle 
from the actual flight path or the initial air- 
velocity vector of the actual round. Mathemat- 
ical studies^ have shown how the parabolic 
constants may be determined for optimum fit- 
ting to the rocket trajectories. Such constants, 
of course, must be expressed, for any given 


rocket type, as functions of the circumstantial 
variables of the firing, or of temperature, air- 
speed, and glide angle. It is found very nearly 
true that the glide angle, the "‘negative eleva- 
tion” or declination of the initial velocity vector, 
affects the trajectory in much the same way as 
for a shell or a bomb. That is, such qualitative 
effects as the rigidity of the trajectory, at shal- 
low angles, are here also evident. Furthermore, 
the degree of gravity-bending is also roughly 
proportional to the horizontal range, being zero 
for an attack out of the zenith and maximum 
for one “on the deck.” 

The longitudinal acceleration of the rocket 
is substantially unaffected except by tempera- 
ture, but this latter variable thus affects the 
whole character of the problem and becomes a 
new variable to cope with if high aiming ac- 
curacy is sought after. All such effects appear 
to depend uniquely on an interior temperature 
of the round, namely that of the propellant 
grain. This governing temperature, although 
responsive via a definable dynamic lagging- 
function to the air temperature, is dependent 
also on the initial temperature determined by 
the conditions of storage ; this latter dependence 
decaying gradually during the time since the 
round was placed into service. The problem is 
not simplified by the variation of air tempera- 
ture with altitude, since while rocket attacks 
are typically made at the lower strata the air- 
plane may recently have been at higher alti- 
tudes. As to time constants, proper to the ab- 
sorption and dissipation of thermal conditions 
in the rocket round, these are, so to speak, of 
the order of half an hour or so. One solution 
which has been proposed, and at least partially 
developed at CIT, for the provision of this sub- 
stantially unmeasurable variable as an input 
to rocket sights, was that of an externally 
mounted thermal model of the rocket. The 
thermally significant part of this dummy round 
would presumably be stored with the standard 
rounds with which it would be used. On the 
whole, however, designers of rocket sights have 
either incorporated the temperature influence 
by means of a manual setting or have ignored 
that variable altogether out of an altogether 
understandable sentiment on the subject. 

As to time of flight as a function of range 


‘'Made by R. M. Peters of Section 7.2 and by per- 
sonnel of AMG-C of AMP. 


• ^ONFIDENTIALU] 


THE RASP ROCKET SIGHT 


137 


along the trajectory, the rocket lies, again, ap- 
proximately halfway between the bomb and 
the bullet. For aiming purposes, particularly 
with regard to kinematic lead, this makes a 
more difficult problem than that of the bullet, on 
the one hand, whereas on the other hand one 
cannot apply the special properties which the 
bomb possesses in this regard owing to its 
preservation of the forward velocity of the 
vehicle. More precisely, the time of flight of 
the rocket, as a function of range, is given ap- 
proximately by 

r = Vatf + Gt‘f 

during the initial burning interval, where Va 
is the airspeed of the launching craft and 
G = G(®) is the rocket’s proper acceleratiori, 
as a function of temperature. In the subsequent 
phase, when burning has ceased, a more natural 
deceleration takes place. This character of the 
rocket, with regard to the relationship between 
range and time for the trajectory, by virtue 
of which it accelerates and then decelerates, has 
special meaning in the problems of aiming con- 
trol. 

THE RASP ROCKET SIGHT 

The project for the development and test of 
RASP has been briefly described in the first 
section of this chapter. There are also very 
complete reports, on the several models of this 
rocket sight which were designed.^ In the pres- 
ent section we may supply some interpretive 
comments from the point of view of other and 
similar developments. Certain component de- 
velopments are worthy of comment since they 
are of more general applicability than to the 
RASP system alone. 

It should be pointed out that this develop- 
ment, which was undertaken before receipt of 
the formal Navy requests for Projects NO-216 
and NO-265, was largely promoted and spon- 
sored by the staff of the Antisubmarine Devel- 
opment Detachment at NAS, Quonset. Assist- 
ance in the procurement of research facilities, 
including the provision of airplanes and other 

'Compiled principally by U. C. S. Dilks, the engi- 
neer directly responsible for this project at The 
Franklin Institute. 


military equipment and auxiliaries for testing 
purposes, was given by that agency in consid- 
erable abundance. In particular, officers were 
permanently assigned to the project, even to 
the extent of setting up residence in the labora- 
tories at The Franklin Institute.^ Following ac- 
ceptance and establishment by NDRC of the 
above named projects, we considered that the 
RASP development constituted part of the 
work they embraced, although new directions 
were then indicated as well. In particular, and 
this viewpoint was early advanced, the educa- 
tional and indoctrinary value of this develop- 
ment was emphasized, since during the initial 
phases there had been almost no experience 
anywhere on the problems peculiar to rocket 
sighting — particularly the automatic variety 
thereof. Thus at least the primary RASP 
equipment was expressly designated as having 
the character of study models, the teachings of 
which would apply more broadly than to the 
project as then contemplated. Initially it was 
felt to be unimportant how complex the system 
was, as long as it could be flown and made to 
function predictably, for then at least the in- 
terrelations among the variables of the problem 
could be subjected to quantitative study under 
practical conditions. It was naturally not over- 
looked that such study models might themselves 
be reduced, as indeed they later came to be, to 
more generally useful form for operational 
purposes. However, the chief contributions of 
this development project were to our knowledge 
of the practical phases of the sighting problem, 
and such knowledge was subsequently applied 
in other developments. 

A diagram of the flow of information in the 
RASP system, from the inputs through the 
various computing components to the outputs, 
is given in Figure 1. All experimental models 
did not include every component and connection 
thus shown ; the diagram in this sense is some- 
what generalized. More precise information on 
the details of such models will be found in the 
contractor’s reports listed in the selected bibli- 
ography hereto attached.'''^-^’ 

For the altitude input an FM altimeter was 

^The promotional efforts and participation of Cap- 
tains Vosseller and Turner may be mentioned in this 
connection, as may those also of Commanders Fiss, 
Edgar, Millard, Swensen, and others. 


GONFIDENTIAI 



IN PUTS 


138 


AIMING OF ROCKETS FROM AIRPLANES 


TEMPERATURE 


ALTITUDE 


GLIDE 00 


AIRSPEED 


(COURSE) 


WINDSPEED 


( WIND \ 
\OIRECTIONy 


TARGET SPEED 


TARGET 

(COURSE) 


AUTOMATIC 

INPUTS 


GRAVITY 

COMPUTER 


RASP 

AS IN VENTURA 


OMITTED IN 
SOME MODELS 


TOTAL 

ELEV 

DEFLECTION 



K SET IN DEPENDENCE 
AIRPLANE - TYPE AND LOADING 


Figure 1. Influence diagram for RASP rocket sight. 


tl 


WXFIDENTI 


OUTPUTS 




THE RASP ROCKET SIGHT 


139 


predominantly employed. No difficulties arose 
on this account from irregularities of terrain, 
the testing and intended operational areas be- 
ing over water. Some doubt was indicated at 
first as to the accuracy of measurement when 
the airplane flew in steeper glides, but that ap- 
parent source of difficulty disappeared, perhaps, 
as was suggested, owing to subsequent altera- 
tions in the antenna designs. Several different 
types of servomechanism were worked out and 
employed for this input, none of which required 
appreciable interference with, or modification 
of, the radio altimeter as such. All such methods 
involved d-c servos, and resulted in shaft rota- 
tions in the computer component in proportion 
to the altitude. 

For the glide angle (y) input, or rather for 
that of the depression 8 of the longitudinal axis 
of the airplane from the horizontal, an appro- 
priate correction being involved for the ap- 
proximations thus introduced, a modified direc- 
tional gyro which was arranged to provide 
rotation in space about a lateral axis, and was 
equipped with an automatic follower, was 
initially prepared as an experimental com- 
ponent. This input was somewhat critical, at 
the shallow glide angles then contemplated, 
owing to the sensitivity of the range, and hence 
of the gravity drop, to the glide when computa- 
tion was effected in terms of the latter variable 
and altitude. A specially equipped gyro horizon 
of Sperry origin, became experimentally avail- 
able however for this application, and was used 
in preference to the above glide-giving com- 
ponent. This horizon had autosyn-detection of 
the gimbal rotation, and provided to the com- 
puter a varying voltage as a function of the 
glide angle. Later several other methods for the 
determination of glide were tried out conjec- 
turally in this project, owing partly to the 
limited aerobatics permitted by the gyro hori- 
zon just referred to. Such limitations, however, 
did not apply as crucially to the bomber-types, 
which were in mind for GRASP, as to the fight- 
ers which were later specified. 

The airspeed, measured in terms of the dif- 
ference between the dynamic and static air 
pressures as in a standard airspeed indicator, 
was automatically fed in by means of a pneu- 
matic follower, although in preliminary models 


this variable was manually incorporated by an 
operator who merely imitated the reading, in 
the position of a knob, of the standard panel 
instrument. Setting of this variable in advance, 
through prediction of the airspeed which would 
be indicated when the firing point would be at- 
tained, was found to be unreliable; and the 
luxury of another operator, in addition to the 
pilot, who might make this setting continually 
under operational conditions, was too much to 
expect. A manually set temperature input was 
employed, however, since automatic means, for 
duplicating the necessary propellant tempera- 
ture of the rocket, were not yet available. 

As to motion of the target in the air mass, 
considered as the vector sum of its motion in 
the water and the local wind velocity, this mo- 
tion was corrected for in RASP, as the kine- 
matic lead thereby required, by separate deter- 
mination of the magnitudes and directions of 
target speed and wind speed. Vector computa- 
tion, mechanical and electrical, was applied for 
this purpose. The directions of wind and target 
motion having once been set in, as by estima- 
tion, on a mock compass scale, these were 
“stabilized'' against subsequent turning of the 
airplane by means of a final setting of own- 
course just prior to the attack when the latter 
course was finally determined. A simple me- 
chanical arrangement was employed for this 
stabilization which had been previously ap- 
plied in a mechanical type of ground speed 
computer. Considerable controversy raged over 
the ability to determine the relevant target mo- 
tion in this manner. At worst, however, the 
magnitudes of wind and target speed could 
always be set to zero, giving no kinematic cor- 
rection as had been originally proposed by Navy 
agencies anyhow, and as in most other sights 
which have been in development. Certainly 
many operators would be able to determine 
these navigational quantities to high accuracy 
and to set from into the computers, but ad- 
mittedly it would be preferable, as in later 
developments, to correct by more nearly implicit 
methods for the motion of the target in the 
air mass. 

The method of computation applied in RASP 
was by attenuators in a-c circuits. To this end 
the several contributory terms of the total aim- 




CONFIDENTIAL 




140 


AIMING OF ROCKETS FROM AIRPLANES 


ing deflection were expressed as products of 
functions of the single and separate input vari- 
ables. The possibility of such expression is of 
course not automatic; it had to be discovered 
and demonstrated. Remarkably enough the ap- 
proximations involved were shown, with little 
trouble, to be sufficiently good. 

The sighting component, or sight head, em- 
ployed in the several RASP systems took on a 
variety of forms. In the first experimental 
model an old retiflector, so-called, was rede- 
signed so that its fixed reticle could be moved 
over the focal plane to cause the emergent beam 
to move bodily in two angular dimensions. A 
system of sliding mechanical ways was in- 
volved, and a small d-c servo assembly was at- 
tached so that the deflections, in azimuth and 
elevation referred to airplane coordinates, 
might be ordered by output voltages in the re- 
motely located computing components. This ar- 
rangement did good service at a time when few 
such remotely manipulable sight heads were 
available. The reflecting collimator represented 
a saving in space, as compared to lenses, al- 
though its position at the top of the final trans- 
parent reflector was found objectionable by 
some, who felt that the sight could thus not be 
called one of the "‘open’" variety. No production 
status was enjoyed by the retiflectors at that 
time, and in order to deal with equipment more 
readily available in quantity, this instrument 
was later replaced as a component of RASP 
by a Mark 30 sight head which we modified in 
somewhat similar manner by moving the final 
reflector. Later yet, a Mark 8 sight head was 
employed, to which was attached, for the eleva- 
tional deflection, a specialties sight unit Mark 1, 
this unit being remotely driven by a voltage in 
the computer in a precisely similar manner to 
that applied before. 

Three distinct models of RASP were pre- 
pared, each with several variants in detail, in 
the course of this project. The first and third 
such models, or RASPS I and III as they were 
called, were much more extensively tested than 
was RASP II. Each succeeding model was 
progressively more compact and more com- 
pletely engineered. Since it was not considered 
sensible to adapt the RASP system to the 
single-seater types which were the principal 


rocket carriers by the time Model III was com- 
pleted, there being then the GRASP project 
well in progress intended specifically for such 
application, it was determined that there was 
no requirement for further development on 
RASP. The personnel and project facilities 
were applied henceforth to the PUSS project. 

^ 4 the grasp rocket sight 

For fighters or other light single-seaters, the 
requirements on rocket sighting equipment 
were more stringent in terms of size and 
weight; the freedom from disturbance, under 
maneuvers, in the component equipment; and 
in the complexity of manual operations which 
are necessary for tactical employment.’^ The 
basic principle of GRASP lay in the method 
whereby the range to the target was recognized, 
as a variable of the aiming problem, in the 
computation of the gravity correction, and, 
potentially at least, of the correction for target 
motion. Assuming that the approach to the 
target occurred in its final stages as a direct 
glide, it was noticed that the arrival at any 
given critical range from the target could be 
signalized by agreement between the altimeter 
reading and a function of the glide angle. The 
deflections having been previously established, 
for this critical or initial range and the glide 
angle and airspeed, etc., in effect, they could be 
kept “up to date” for shorter ranges by a 
chronometric input-motion initiated when the 
critical range was encountered. In preliminary 
models the said initiation was to be manually 
made, by the pilot when he noted coincidence 
of a pair of indicators, whereas in later models 
an automatic initiation was embodied which 
simultaneously signaled to the operator the 
closing of the range to that degree and the 
entry into the continuous-firing regime. 

Two principal developmental models were in- 
volved, called GRASP I and GRASP II. Ex- 
tremely complete reports on the course of the 
research itself, as well as on the elaborate 
testing program which was undertaken and on 

^As one of a number of proposals made to meet 
these requirements, one made by E. C. Cooper at The 
Franklin Institute, for the system which became 
GRASP, was accepted and was embodied in a de- 
velopment program in which Cooper, among other 
duties, was project engineer. 


^rONFIDENTTALjl’ 


THE GRASP ROCKET SIGHT 


141 


the final equipment, were regularly issued by 
the contractor. Reference to certain of these 
reports will be found in the bibliography of 
this chapter.' ® From the beginning the Navy 
Project NO-216, under which we formally op- 
erated, covered the development of the GRASP 
system. GRASP 11 was finally designated air- 
craft rocket sight Mark 2, when taken together 
with the gunsight Mark 21 or gunsight Mark 
23 which it employed as sight head, and the 
GRASP 11 computer component was designated 
computer Mark 35. While other output com- 
ponents than the said gunsight might equally 
well have been applied as means whereby the 
pilot’s aiming indicia were to be automatically 
deflected, it was the plan of the GRASP project 
to use the gyro gunsight in this manner, as it 
was also the expressed desire of the Service 
request which preceded the project designation. 
The purpose of this combination was simply to 
permit a semi-universal sighting arrangement, 
at least for gun and rockets, with rapid change- 
over capabilities between the two functions. As 
before remarked, this gunsight did not receive 
wide application in Navy airplanes, as it hap- 
pened, whereas a similar Army gunsight was 
widely installed and applied. A modification of 
GRASP II was consequently prepared, in the 
latter part of the development, under Army 
Project AC-121, but at the close of World War 
II had not yet been tested under Service 
auspices. 

Some remarks on the components of GRASP, 
and on their systematic arrangement, are prob- 
ably here in order. A ‘‘flow diagram,” Figure 
2, is here included to illustrate the handling of 
the data by the computing system. The tem- 
perature and the airspeed were manual inputs, 
although it had variously been planned that 
airspeed might be automatically provided, by 
means now well known, or again that airspeed 
might adequately be correlated with the steep- 
ness of glide — and in consequence automati- 
cally incorporated therewith. It was opined that 
the presence of a manual setting attracted the 
pilot’s attention to the rigors of making a 
prediction as to his airspeed when firing was to 
occur, and that his impression of how precisely 
this variable must be set for accurate aiming 
was exaggerated. 


The altitude, as we have implied, was not set 
in continuously but was recognized in terms of 
the instant when this variable agreed with the 
glide input in determination of the initial range. 
In the first model such recognition was by the 
operator, whereas in the second model it was 
automatic and involved only a contact arm on 
the “slow” indicator arm of an auxiliary baro- 
metric instrument. This component, installed in 
a small (approximately 4x4x8 inches) single 
computer box, was provided with adjustments 
for target altitude and the barometric pressure 
at sea level. Establishment of electrical contact, 
at the initial or critical range, set in motion the 
chronometric sequence of the computation. The 
latter was delivered mechanically by automati- 
cally wound clockwork, which returned to the 
initial position and latched itself when the op- 
eration was completed. 

The most elaborate component of the GRASP 
system was that which provided the input of 
glide angle, or the airplane pitch as an approxi- 
mation thereto. This comprised a captured 
mass, or captured pendulum accelerometer, so 
aligned in the airplane that the total (gravity 
plus inertia) acceleration, in the direction of 
the airplane’s vertical axis, is thereby mea- 
sured. A servomotor, actuated by special 
damped and overriding contacts connected to 
the pendular structure, rotated a spring in a 
degree sufficient continuously to hold that struc- 
ture essentially stationary in a framework, the 
rotation of the spring then being taken as a 
measure of the acceleration. Although the ac- 
celeration thus measured was only proportional 
to the cosine of the pitch or glide in straight 
flight, the effect of curvature of the airplane’s 
path was not fatal since (1) it was in the na- 
ture of a prediction of future glide angle, so to 
speak, and (2) it tended to a partial compensa- 
tion, ^ in the elevation direction for motion of 
the target in the air mass. To guard against 
fortuitous accelerations, having no real sig- 
nificance for glide, a limiting speed was in- 
corporated in the servomotor, and to avoid 
extremes such as incurred when the airplane 
entered the dive a cutout was included which 

'Noticed first by H. Whitney of AMG-C, after whom 
it was sometimes called the “Whitney effect,” of 
which in fact there were several others. 


FIDENTIAL 


I N P U TS 


142 


AIMING OF ROCKETS FROM AIRPLANES 


*• 


TEMPERATURE 


* 


AIRSPEED 


GLIDE ( ) 


ALTITUDE 


TIMER 


AUTOMATIC 

INPUTS 


GRASP 

AS IN HELLCAT 


COMPUTER 



GLIDE DERIVED 
FROM FEEDBACK 
ACCELEROMETER 


OPERATION OCCURS, 
STARTING TIMER, 
WHEN h AND S 
AGREE THAT THE 
INITIAL RANGE 
R = Ro 

IS ATTAINED 


SIGNAL ALSO 
GIVEN TO PILOT 


COMPUTER 


Fh(t,6 ) 


H- 

3 

Q. 

H 

3 

O 


MULT 


TOTAL 

ELEV 

DEFLECTION 



CONSTANTS FOR ROCKET 


(5.00"hVAR; 11,75" AR) 


Figure 2. Influence diagram for GRASP rocket sight. 






THE PARS ROCKET SIGHT 


143 


was operated automatically under excessive 
accelerations. 

Computation of the several functional rela- 
tions in GRASP was accomplished by logarith- 
mic cams. The output, as an aiming deflection 
in elevation, was developed by rotation of a 
resistor in the trail coil circuit of the gyro gun- 
sight Mark 23. Trimming resistors, of fixed but 
adjustable values, were involved in switching 
circuits to allow the use of different rockets, for 
which, incidentally, it was found that the total 
deflections were sufficiently expressible, rather 
surprisingly, as functions of one another di- 
rectly. Employing a large current in the range 
coil, the reticle could be deflected over the whole 
range, it was discovered, by alteration of the 
trail coil current. This worked, in fact, for both 
coordinates, and the relationship between an- 
gular deflection and the ratio of trail coil cur- 
rent to the then existing range coil current 
was found to be adequately linear. Further, a 
method was worked out™ whereby this ratio 
could be set by linear manipulation of a single 
low-power resistor placed in special bridge cir- 
cuit. This technique was valuable in maintain- 
ing the desired compactness of the computer, 
of which the total size has already been re- 
ferred to above. For installation, such as those 
made for trials in the F6F, it was only neces- 
sary to remove the standard cable connector of 
the computing gunsight and insert a two-way 
adaptor on a new cable leading to the GRASP 
computer. 

’ 5 THE PARS ROCKET SIGHT 

We shall not give an exhaustive description 
of this development, although it has been one 
to which great promise was attached. The his- 
torical circumstances of the project were al- 
ready referred to briefly in this chapter. It was 
planned that in this system not only an ex- 
tremely simple and compact computer should 
be involved, with very little else, but that at 
the same time the solution carried out thereby 
should be most complete and automatic. The 
computation was all mechanical, involving small 
linkages of a type later embodied in PUSS, al- 
though in one model the output motion affected 

■"By E. Cooper. 


setting of a light potentiometer, as the variable 
according to which remote transmission to the 
sight could be accomplished. Physically, the first 
experimental model of the PARS computer was 
constructed entirely within the case of a stand- 
ard barometric altimeter, of which the motion 
of the aneroid capsule provided one mechanical 
input to the miniature computing linkage. Air- 
speed entered the computation similarly (see 
Figure 3), a dynamic-pressure diaphragm be- 
ing placed in the same case, the ambient pres- 
sure in the latter being the static or barometric 
pressure as needed both for altimetric and air- 
speed measurements. The temperature variable 
was manually set into the instrument, although 
at one time it had been considered likely that an 
adequate correction for temperature could be 
accomplished by inclusion, in the linkage, of a 
small bimetallic “motor'' which would respond 
with some delay to the external air temperature 
via the static-pressure line. 

The accelerometer component, whereby the 
steepness of glide or dive was detectable by the 
PARS computer, deserves special mention. It 
constituted a spring-constrained mass, on a 
pivoted arm which lay normally and approxi- 
mately in the plane of the wings of the airplane, 
and which moved out of a normal position in 
response to the total acceleration in the air- 
plane's “apparent vertical." The free arc- 
motion of the constrained mass, which was 
damped by a pneumatic carbon-chromium dash- 
pot, formed one direct input to the computing 
linkage. A number of experimental models of 
this component were prepared and tested, both 
in the laboratory and on flight tests arranged 
solely for this purpose, under conditions which 
allowed comparison of the acceleration record 
of this component with that derived from the 
readings of other instruments used for calibra- 
tional functions. 

In an early form of the PARS instrument, 
it was contemplated to reduce the system to its 
ultimate and basic instrumental simplicity by 
displaying, on the instrument panel only, a 
mock reticle-pattern representing that included 
in a fixed infinity sight, and on the mock pat- 
tern a moving point corresponding to the cor- 
rect position, in the real reticle pattern, at 
which the target should be taken for effective 


'l^ONFIDt:^>mAL ^ 


]44 


AIMING OF ROCKETS FROM AIRPLANES 


fire. Thus the output defiection, which might 
normally be transmitted to a manipulable sight 
head as the aiming deflection, would here 
merely move a visible indicator on the face of 
the computer, the latter to be incorporated as 
a standard panel instrument. Owing to the 


indeterminacy of skid, which affected almost 
one-to-one the azimuth aiming errors with any 
existing types of sight, made it unworthy to 
add much complexity to the computer for sake 
of that dimension. This question of skid has 
been controversial indeed, and was only be- 




NORMAL 

ACCEL 


PARS 

AS FOR THUNDERBOLT 



Figure 3. Influence diagram for PARS rocket sight. 


many voices raised in objection to this plan, it 
was later resolved (perhaps wrongly) to em- 
ploy the now more orthodox technique, and to 
“servo” the output of the computer, resistively 
recognized, to one of the available sight units. 
Only an elevational deflection was thus con- 
cerned, there being no azimuthal computation 
in PARS. While an inherent computation oc- 
curred in elevation for target motion, at least 
over a central band of glide angles, owing to 
the accelerometric sensitivity to curvature of 
path via the glide measurement, no similar cor- 
rection was evident for the azimuth component. 
It was considered by many, however, that the 

f 


ginning to come under an articulate quantitive 
study, by the agency of a testing program, 
toward the close of hostilities. We shall not 
here add our own prejudices to those in evi- 
dence elsewhere. Works on the subject by 
AMG-C and AMG-N, of AMP, are recom- 
mended to the interested reader. If the skid 
problem cannot be simply resolved, either by 
aerodynamics or by instrumental means in com- 
putation, then this certainly is one of the larg- 
est objections to the finned rocket as a weapon, 
which behaves in this connection almost op- 
positely to that of a bullet or shell. Our own 
view of this problem is a generally optimistic 


gnfidentia: 





PUSS AND SOME COMMENTS ON THE FUTURE 


145 


one, but admittedly the next step is to arrange 
to have reliable data at hand. We appear to have 
digressed somewhat from PARS, to which we 
now momentarily return. 

There was not time, during the project thus 
far, for extensive or definitive firing tests on 
the PARS rocket sight, which incidentally be- 
came officially aircraft rocket sight Mark 3, 
and simultaneously computer Mark 36. Me- 
chanical failures, arising from vibratory con- 
ditions not adequately foreseen and guarded 
against, were experienced on several earlier 
flight tests. PARS remains a highly ambitious 
attempt to compress a fire-control system to 
insignificant dimensions, and the technique is 
certainly of future value. Thus for example the 
lessons there acquired at some pains are well 
learned if they are applied in such broader and 
more futuristic programs as that of the con- 
tinuing PUSS project. 


^ 6 PUSS AND SOME COMMENTS ON THE 
FUTURE 

We have referred freely to the PUSS project 
at numerous other points, and Chapter 10 is de- 
voted exclusively to that topic. PUSS, however, 
is fundamentally an aiming-control system for 
rocketry, at any rate that was the primary pur- 
pose for which the computing method was pro- 
posed and developed. While also a bombsight 
and a gunsight, as occasion may demand, the 
most general and most difficult aiming problem 
solved by this system is that for the rocket, and 
in this sense it is believed that the project is 
unique. 

For future development the following courses 
are suggested: Without losing sight of the 
universality toward which this system was 
directed, it would be wisest to concentrate first 
on the rocketry phase, and to press the develop- 
ment to a testing status for that weapon alone. 
As the one type of rocket on the basis of which 
the assessment should be made, we should 
choose the 5."00 HVAR in preference to the 
11. "75 AR, owing to the better state of present 
knowledge of the characteristics of the former. 
As to subsequent development and testing of 
the system as a gunsight, considered as an 


adaptation of its function in rocketry, consid- 
eration should be given to lower projectile veloc- 
ities and longer ranges, and consequently to much 
longer times of flight, in view of the probable 
coming into importance of low-velocity, high- 
caliber shells, which may, indeed, replace the 
present rocket types for airborne fire control. 
Here we are thinking, for example, of plane-to- 
plane combat, where the rocket now presents 
an aiming problem of very great magnitude. 
For bombing, on the other hand, thought should 
be spent, if it is at all on PUSS, in the direction 
of a bombing tactic in which a firing course, or 
rather a release course, is followed. With the 
greater downward vision and possible aero- 
nautic alterations in airplanes, the practical 
advantages of toss bombing may disappear. 
Furthermore, not only is such a manner of 
bombing one which may be controlled by a 
system which is a special case of the present 
PUSS rocketry computer, but it may be made 
inherently more accurate by being, as are the 
other PUSS computations, less sensitive to all 
the inputs other than angular rate. 

There will be a great advantage in a uni- 
versal aiming control based on a uniform meth- 
od for all types of projectile, since then the 
same basic components may be most fully 
utilized for all applications, thus leading to 
smaller, lighter, and simpler instrumentalities. 
Furthermore, it would thus be simplest to 
adapt the system, once developed, to the newer 
missiles as they appear. Aside from possible 
radar inputs, for blind operation and for rang- 
ing data, there are not many other basic items 
of primary data. It appears worth while in this 
vein to arrange for supplying all such inputs, 
comprising dynamic and static pressures, ac- 
celerations in all directions and of both primary 
types, and the angular rates of the vehicle in 
space, in a compact universal input assembly. 
Whatever firing or computing methods are em- 
ployed, they will be most efficiently based, at 
least statistically and ideally, on the maximum 
number of available inputs, so incorporated in 
the sighting method and in the computers that 
the overall errors are minimized. In any case 
it will be easier in the future to omit a given 
input than to include it by modification. This 
may seem a naive philosophy, but it is based 




ONFIDENTIAL 


146 


AIMING OF ROCKETS FROM AIRPLANES 


on a certain amount of experience, nevertheless. 

It is recommended further that a study be 
made of the usefulness of higher-order linear 
operators in the dynamic computer of PUSS, 
for all weapons being considered. This is an 
almost entirely unexplored field, and may con- 
tain many treasures, in terms of reduced track- 
ing time, stability, and accuracy. It may also 
be found that such problems as skid are re- 
solvable implicitly when the more general dy- 
namic forms are resorted to. In this study, the 
electronic simulative techniques will probably 
prove invaluable, as they have in other and 
analogous fields of effort. The pilot’s tracking 
simulator, now in its initial form, is to be 


placed in operation at The Franklin Institute 
very soon, and should provide a nucleus of the 
simulative apparatus whereby the more recon- 
dite dynamic questions may fruitfully be 
studied. To name an example of the instru- 
mental possibilities for future appraisal, by this 
and other means, we mention the general plan 
of recognizing, as inputs to such computing 
systems as that of PUSS, the motions during 
flight of the control surfaces. Especially with 
the greater symmetry which may be attained 
in jet-propelled flight, these motions may be 
found highly significant when applied by retro- 
active processes in the dynamics of advanced 
aiming controls. 


f 



Chapter 10 


INTEGRATED EQUIPMENT FOR THE PILOT 


1 HISTORICAL REVIEW OF THE 
DEVELOPMENT 

A S WORLD WAR II progressed, several trends in 
the application of warplanes became evi- 
dent. One of these involved the increasing use 
of the lighter planes, such as fighters, for such 
purposes as bombing and rocketry. There was 
of course the dive bomber, as a classical type, 
but whereas the German Air Force had used 
this type strategically, in a sense, the American 
version was only in the Navy and was employed 
tactically against ocean targets. Strategic 
bombing by fighters was actually employed by 
the Navy in the Pacific war, witness for ex- 
ample the bombing of Tokyo from carriers. 
Part of the trend, both in Army and Navy, and 
we need speak only of tactical warfare, was 
more particularly in the more diversified ap- 
plications of the single-pilot types. Consider 
the activities of the Hellcat and the Corsair, 
in the Navy, and of the Mustang, Lightning, 
and Thunderbolt, in the Army. For strategic 
support, almost in every type of attack, these 
planes became nearly predominant. They op- 
erated as regular fighters, both for escort and 
interception, or simply, and especially toward 
the end, merely patrolling for quarry of any 
type. They carried bombs to strategic ranges, 
releasing them in gliding and diving attacks. 
They were rocket carriers, bearing as many as 
eight rounds apiece, from the 2."25 SCAR (for 
practice) to the 11. "75 AR. Such airplanes were 
impressively potent and versatile. Against 
ground targets especially, whether for support 
or on independent forage, they could strafe, 
with gun and cannon, drop bombs, and launch 
rockets from ranges measured in thousands of 
yards. The desire for, and evident benefits of, 
such flexibility of function is of course apparent 
in the airplane types which have appeared. A 
notable early example was in the TBF Avenger, 
which although not too impressive as a fighter, 
could carry torpedoes, bombs, and rockets. 

A number of us, noticing this trend in a 


broad sense, and having other reasons to wish 
for a more generalized approach to the instru- 
mental problem of aiming controls, argued for 
the development of systems which would apply 
optionally to the several weapons coming into 
use by the same vehicle.^ An important premise, 
in support of the possibility of such a widely 
applicable single system, was the evident sim- 
ilarity among the fundamental solutions to 
which the fire-control problems of the various 
projectiles were amenable. Thus typically ab- 
solute angular rate was increasingly useful in 
this field, for several types of inherent compu- 
tations, and progress had been made and was 
promised in new components for the measure- 
ment and delivery of this variable. In the case 
of other variables too, these appeared as inputs 
in more than one of the numerous proposals 
being made for bombing and later for rocketry. 
An obvious saving was thus possible through 
combining input components in a universal 
system. Further, it was considered essential 
that a single, universally applicable sight head 
be made available, to which the outputs of the 
various computations could be selectively con- 
ducted, and for which the very difficult installa- 
tion problems, on each form of airplane, could 
be engineered once and for all. Not the least 
advantage contained in the flexibility of this 
general mode of design — and this is empha- 
sized particularly in retrospect, it was not at 
first insisted upon or indeed as vividly realized 
— is the freedom whereby future developmental 
changes might be incorporated. None can fore- 
see either the newer circumstances which will 
obtain in the future, as the novel instrumental 
and theoretical techniques which never cease to 
emerge. To design in expectation of such change 
is the wisest course; to freeze as many com- 
ponents as possible and to leave their interrela- 
tions more arbitrary was one of the precepts of 
Project PUSS, and remains a valid criterion 

“The present writer remembers conversations on this 
topic, at an early state, with Commander E. S. 
Gwathmey (then) of BuOrd. 


(5 


ONFIDENTIAL 


7 


147 


148 


INTEGRATED EQUIPMENT FOR THE PILOT 


today, especially in multipurpose aiming con- 
trols. Where inputs, computers, and outputs are 
too innately combined, such alterations, to fit 
new weapons or tactics or instrumental theories 
and techniques, are a more serious task. 

In any sight for fighters an inevitable prob- 
lem is that of reducing the amount of added 
equipment placed in front of the pilot, not that 
space and weight restrictions are liberal at 
other locations in the airplane, but the space 
around the instrument panel comes highest of 
all. This was part of the reason for wanting a 
pilot’s universal sight head, which with its 
servo equipment could be remotely operated by 
equipment at other points, and which would be 
designed down to the minimum size and incon- 
venience compatible with effective operation. 
With modern servos there should be no trouble 
in attaining, by this means, all the smoothness 
and precision and other requirements of per- 
formance which could be desired. There is much 
more to be said on the question of the sight 
head, but such dissertation can be better rel- 
egated to sections, in this chapter and else- 
where, on specific parts of the project. We refer 
here altogether to visual operations rather than 
to blind attacks. In rocket sights and in the 
PUSS project radio detection was considered, 
by us, only as a potential means for measuring 
altitude, and possibly range, as inputs. In any 
case the designer of fire controls has found him- 
self faced with many problems which were 
posed by the constructional peculiarities of air- 
planes, and particularly of fighter airplanes. 
Whether or not some of these peculiarities were 
essential is another question, but one of the 
measures which would permit circumvention of 
such problems was the proposed universal sight 
head, to be perfected as such and to be deflected 
automatically, referring to the relative direc- 
tion of the line of sight thereby established, by 
remote components of whatever nature. 

As a group we brought to the problem of 
planning and building a pilot’s universal sight- 
ing system, referred to henceforth as PUSS, 
experience in the development of computing 
gunsights, rocketsights, and bombsights, which 
was to serve as valuable background. We had 
worked also on the problems of reducing the 
size and weight of computers, and of designs 


which did not require high-precision manufac- 
ture. The projects, then still in progress, for 
the rocketsights RASP, GRASP, and PARS 
were considered as contributory, not only since 
similar problems in design were there being 
met, but because any of the techniques em- 
ployed therein for solution of the rocketry aim- 
ing problem were valid candidates for the 
rocketry phase of PUSS. The newer proposal 
for the central rocket solution, based predom- 
inantly on absolute angular rate, was relatively 
untried, but its conjectural development was 
thought to have a promise worth the gamble, 
since the more orthodox methods of earlier 
projects could be resorted to rapidly if the 
gamble turned out poorly. For plane-to-plane 
gunnery it was planned to use the well-known 
first-order principle involving angular rate and 
range, although it was hoped that higher-order 
methods might provide a better compromise be- 
tween precision and stability of tracking, on 
the one hand, and that certain rangeless meth- 
ods, on the other hand, would ultimately be 
applicable. Mentioned briefly in Chapter 1, 
such methods are based even more crucially on 
angular rate criteria. It was considered, any- 
how, that a simpler instrumental problem was 
involved, and that apparatus which might solve 
completely the problem for rockets could be 
specialized rather readily to bullets or cannon 
shell for air-to-air combat. For strafing as a 
gunnery operation, the need for computing 
sights was not given prominence, although with 
rangeless methods, again, and these appeared 
particularly applicable here, the question was 
held open. How to handle the bombing solution 
was a major question, since the logical use of 
the angular rate principle for gravity-drop 
correction was unusable in typical airplanes at 
significant range, the superelevation allowance 
being greater than the available downward 
vision. For this reason, and owing also to cer- 
tain psychological preferences which appeared 
to be evident, and further to some problems in 
the stability of flight with existing airplanes, 
we chose to consider toss bombing as the meth- 
od for PUSS. While the gravity drop is not 
allowed for by the methods of absolute rotation 
in the preferred procedure for toss bombing, 
such methods do appear for the target motion in 


t 


KonftdentiaI 


REMARKS ON THE HUMAN PROBLEM 


149 


this problem, and it was planned to capitalize 
on the presence of gyro reference equipment 
incorporated in the PUSS system for the other 
functions. 

The initial experiments on a unified PUSS 
computer involved a free gyro as basic com- 
ponent. By various processing arrangements 
such a gyro was to be alternatively caused to 
rotate about a horizontal axis in space, for 
gravity corrections, or to “pursue” an index 
for synthesis of a disturbed sight. It was recog- 
nized that both such modes of operation might 
be followed simultaneously. It was soon found 
precisely how to generalize the classical com- 
puting sight to give the more general solution 
for rocketry, with all major corrections. There 
are three : the gravity drop, target motion, and 
aerodynamic error. Although these may be con- 
sidered as independent angular corrections, 
when they are to be developed by angular rate 
methods their functional independence disap- 
pears and separate and additive consideration 
is impossible from the instrumental standpoint. 
The theory involved the addition, in the equa- 
tion of a lead-computing sight, of terms inde- 
pendent of the rapidly changing variables, or 
in other words of the lead itself and the angular 
rates in space of the line of sight and of the 
thrust axis. A full-scale program for reduction 
of this method to practice has now been in 
progress for about one year, and has followed 
several parallel paths in terms of the philosoph- 
ies of apparatus. Fully captured gyro systems 
have gradually replaced the partially captured 
systems which were earlier contemplated, a 
number of experimental designs of both types 
have been undertaken. Several choices are still 
evident among the other inputs, it being pos- 
sible for example to measure glide either from 
the rate of change of altitude, altitude itself, 
and airspeed, or from the indication of a stable 
gyro horizon. 

Further on the captured-gyro angular rate 
components, there is still a choice as to whether 
null methods or purely mechanical constraint 
and sensitive detection should ultimately be em- 
ployed. Both types of instrument have been 
built, and the final selection depends on the 
nature of other components. In a larger con- 
nection, both electric and pneumatic techniques 


in instrument design have been continued to- 
gether, and neither has as yet proved demon- 
strably inferior. Mechanization of the static 
functions in the system, as contrasted with the 
dynamic differential equations which must be 
embodied, have been made by means of small 
linkage-computers (see Chapter 5), and this 
type of computing component is planned for 
both the electric and the pneumatic version of 
PUSS. 

Most of the above development, for which 
Navy Project NO-265 had been assigned, was 
conducted at The Franklin Institute.*^ In the 
meantime, the electronic flight simulator (see 
Chapter 4) was being prepared at Columbia, 
and had incorporated the principal dynamics of 
the PUSS computer as well as the character- 
istics of flight which would be invariant for all 
such computing methods which might be pro- 
posed. It was hoped that this simulator would 
soon become available for tracking studies along 
with the instrumental phases of development, 
but developmental work on the simulator, aside 
from the consolidation of existing components 
and the preparation of a descriptive report, 
ceased by October 1945. However, it is planned 
to move this equipment to Philadelphia where 
the remainder of the PUSS project will con- 
tinue under a direct Navy contract. Although 
at the present only rudimentary flying opera- 
tions have been successfully simulated, there is 
no question but what the more intricate ques- 
tions of stability, such as that of the rapidity 
of subsidence to a solution under manual opera- 
tion, can be submitted to experiments upon this 
apparatus in the laboratory. A means will thus 
be available for exploratory alterations without 
the expense and duration of full-scale testing. 

2 remarks on the HUMAN PROBLEM 

In the development of generalized aiming 
controls for the pilot, particularly where he is 
the lone occupant of the airplane, it must be 
well recognized what burdens can and what 
burdens cannot be placed on such an individual 
as participant or impresario in the ceremonies 

‘’The project engineer concerned was J. A. Bevan. 
M. Golomb was a prominent contributor there, on 
mathematical, experimental, and general design 
phases. 


UCONFmENTIAI? 


150 


INTEGRATED EQUIPMENT FOR THE PILOT 


of practical utilization. The development en- 
gineer cannot dispense with this realistic back- 
ground to his problem, although his thinking 
should not thereby be limited; he should talk 
with fighter pilots extensively and intensively, 
hearing although not necessarily believing all 
they have or can be persuaded to say. He should 
thus try to determine the common denominators 
among the sometimes widely disparate opinions 
of such experienced pilots, and to find out, not 
so much what they want but what they need. 

Note that the fighter pilot is a high type of 
individual, the select survivor of a series of 
rigors in training and combat. Such a man is 
at the height of his prowess, in the matters of 
undeliberating brain and nerve. He is old, for 
his kind, at the age of 25. But he is hard beset. 
For not only must he be the master, in modern 
combat, of several specialized weapons of at- 
tack, but also he must be navigator and tac- 
tician as well, and an expert at recognition and 
deception. As captain and crew of his craft, the 
modern fighter pilot must be self-sufficient. 

It will readily be evident that the fighter 
pilot will not greatly exert himself to ob- 
tain computing apparatus which adds to the 
complexity of his already gadget-ridden exist- 
ence, unless his survival is otherwise and com- 
pensationally made more likely. This view, of 
course, is by no means universal, even among 
fighter pilots themselves. However, it is com- 
mon enough, and not without certain justifica- 
tion. 

Specifications for aiming controls, such as 
proposed in Project PUSS, are affected by such 
considerations as those above. While these have 
been written out more completely elsewhere 
(Section Re8c BuOrd), by the present writer 
and others, we mention some highlights here 
since they may apply more broadly than to this 
single project: No manipulations should be 
required of the pilot, other than those of flying 
and firing, during the attack — with whatever 
weapon. Only rudimentary instrumental manip- 
ulations should be required at any time prior 
to the attack. The pilot should further be free 
to fly in any manner he chooses until he steadies 
out on the attack itself. This is for evasive 
purposes, and for selection of a propitious mo- 
ment or location for pushing the attack to its 


crisis. Any approach which requires an inflex- 
ible routine, or pattern of elements, is doomed 
in advance. The sighting or computing system 
should not require any intellectual gymnastics 
by the pilot at any phase of the operations. To 
expect him to “go into the literature’’ via tab- 
ular data, or to make even the most trivial 
calculations by slide rule or nomogrammic 
computers, is to impose a burden which may be 
intolerable. All adjustments should be localized 
and arranged mnemonically and unmistakably, 
and there should never be any question of what 
to do, or whether any given operation, once 
made, was the proper one. 

10.3 xHE PILOT’S UNIVERSAL SIGHT 
HEAD 

This important component of a universal 
sighting system, relatively speaking, can be 
considered somewhat independently of the oth- 
ers, especially if only a simple reticle as aiming 
index thereby is to be displayed, movable auto- 
matically on a two-dimensional field of solid 
angle. Such is not the case, of course, when 
multiple reticles are involved, as in the pro- 
posed Texas Sight or in certain other proposed 
constellation displays where the relative motion 
of a pattern with the target is to be made zero. 
Again it is not the case when a ranging ring 
must be used, as in the classical lead-computing 
sights. It has been the policy in PUSS, however, 
to hope either for automatic ranging, as with 
ARO radar or Pterodactyl, or for aiming meth- 
ods in which the range does not explicitly 
appear (see Chapter 1). Another complication 
is the expressed and understandable desire for 
the availability of a fixed sight, which inciden- 
tally is a sort of “universal fire-control system” 
in itself, for standby or other purposes. This 
matter further divides itself into the cases in 
which a fixed reticle is to be maintained simul- 
taneously visible with the moving reticle, al- 
though perhaps optionally illumined, and the 
cases where it is adequate to operate a control 
which “freezes” the moving reticle in its bore- 
sighted or fixed zero position. Ideally it should 
be possible to do all these things, and also to 
set a fixed deflection other than the zero one by 
a calibrated adjustment. In the physical ar- 


THE PILOT’S UNIVERSAL SIGHT HEAD 


151 


rangements whereby a fixed reticle may be op- 
tionally available, this is best accomplished 
by a mechanical connection capable of very 
rapid operation, since such a standby sighting 
facility may be desired owing to failure of 
servos, etc., and it is questionable to expect an 
electrical adjustment then to be workable. Re- 
buttals to this, in which it is claimed that under 
such failures the reticle lamp will be lost also, 
are only partially valid. This quick and fool- 
proof “throw over” criterion, in any case, has 
been upheld thus far for the PUSS system. 
Within PUSS, the pilot's universal sight head 
has been known as PUSH. 

In the PUSH developments to date, as a sub- 
division of Project PUSS, the principal ap- 
proach has been to manipulate a plane mirror in 
a collimating sight. Very different problems are 
encountered, depending on whether the (single) 
mirror is placed in the divergent beam from 
the reticle or in the subsequent beam from the 
collimator, the latter being either a lens as- 
sembly or a shaped mirror. In the former case 
the mirror-driving component must compensate 
for the angular aberrations of the lens, but 
here the mirror itself may be fairly compact. 
In the latter case, with the mirror outside 
in the beam which is focused at infinity, an 
exact type of geometry^" may be employed. 
In both cases the finally collimated beam 
is reflected back to the pilot from a “trans- 
parent” reflector, which may be specially 
introduced or may be the windscreen of the 
airplane itself. The illumination problems in- 
volved here are considerable,** to cover the range 
of ambient intensity which is encountered, un- 
less either a sun screen can be placed in front 
of the entire system, or a combination of lower 
transmission and greater reflectivity may be 
attained for the final reflector, and simultane- 
ously a correspondingly lower transmission for 
the whole canopy. Furthermore, the problem 

•"See the application of the Orthopentax as shown in 
Chapter 5. 

^Although, as we may note here, the attractive sug- 
gestion has been made that an intermittent gaseous 
discharge might provide a more intense illumination 
of higher optical efficiency, that is to say with smaller 
dissipation of heat, this question is still somewhat 
controversial. Additional equipment would be required, 
but this might add only fractionally to the computing 
system already contemplated. 


of eye relief is nearly insuperable with the 
orthodox systems. A poor compromise must be 
accepted between the blocking of forward 
vision and the width of the emitted beam, in 
typical instances. One way out is the avoidance 
of collimating lenses through application of 
reflex collimation, as for example in the Bowen 
Sight (Mount Wilson). Another is to bring the 
final reflector, then having small dimensions, 
near to the pilot’s eye, and perhaps to allow it 
to move about with his head, being maintained 
in direction by a stabilizing system. Probably 
the best measure of all is the use of a forward 
“periscope” or one-to-one telescope of wide 
angular field (again Mount Wilson) and of 
large aperture and eye relief. This solves many 
problems at one blow, but is highly unorthodox. 
It would be possible to arrange for all the pilot’s 
forward vision to pass through this telescope, 
which might allow, say plus or minus 25 degrees 
of angular vision in every direction, might be 
bulletproof, and would permit better stream- 
lining through the elimination of the flat wind- 
screen. Such a telescope has two focal planes, 
so that reticle motions and other desired indicia, 
focused at infinity, such as the whole instrument 
panel around the edge of the field, could readily 
be incorporated. Opaque reticles, automatically 
solving the illumination problem against bright 
backgrounds, could be illuminated laterally by 
known methods for dim operational conditions. 
Ultimately such a telescope might well be a foot 
in diameter, extending from the pilot at the 
center of gravity to the nose of the plane. The 
weight imposition, owing to the large glass or 
plastic lenses, would not be serious to the imag- 
inative planner, since this object would literally 
be worth its weight in gold. Think, for example, 
how easy it would be to include an image of the 
radar scope in the field! This whole possibility 
is not altogether original® with the writer, but 
is an extension of much older proposals. Its 
consideration for future development is most 
heartily recommended. 

To return to the rather more nearly earth- 
bound topic of past developments on PUSH, a 
program of mirror-linkage design was carried 
on both at The Franklin Institute and at The 
Bristol Company, although not on a tremendous 

*See, for example, T. Dunham, Jr. of Section 16.1. 


(S 


GONFIDENTIAI 



152 


INTEGRATED EQUIPMENT FOR THE PILOT 


scale. Experimental designs were prepared, for 
the (single) mirror placed both “inside” and 
“outside” the collimating lens. For the avail- 
able optics, the former method was ultimately 
given up, owing to the compromises which were 
necessary in the ability to meet specifications, 
as to focus, field, and precision, which had pre- 
viously been agreed upon. Furthermore, this 
method was explored by Navy at Specialties, 
Inc., who found a rather good compromise and 
are preparing an initial model for experimental 
application to PUSS; the cooperation is of- 
ficially via BuOrd. A number of mirror linkages 
were developed under our own direction, prin- 
cipally for the second method, which gave great 
accuracy over a field of plus or minus 15 de- 
grees. Models had been installed, with large col- 
limators, in cockpit replicas at Philadelphia, 
and the design of housings of practical types 
was about to be considered when the project 
began to close. Presumably such development 
can be continued under Navy auspices if it is 
desired. The interested and authorized reader 
should study also the sight head designs of the 
Draper-Davis A-1 sight in the Army. For fu- 
ture development, however, we urge that a 
much longer view be taken of this whole prob- 
lem, and that the conjectural methods men- 
tioned above should be considered along with 
newer proposals which most certainly will be 
received. 

A very interesting possibility is in generaliza- 
tion of the fly’s eye collimator, so called, which 
is described in contractor’s reports by Eastman 
Kodak and The Franklin Institute, to give a de- 
flectable reticle-image. (See the report of Divi- 
sion 16.) 

Whatever the nature of the sight head, if it 
is of the universal type here referred to, remote 
followers or servomechanisms must be em- 
ployed to deflect the line of sight in obedience 
to the outputs of computers placed at some 
distant points. The reference variable at the 
sight head may be a resistor or capacitor, say, 
in the case of electric servos. For d-c servos the 
resistor is very convenient, and has been em- 
ployed by us and by Specialties, Inc., in experi- 
mental models. The capacitor follower, how- 
ever, for a-c circuits, permits extreme fineness 
of setting, and consequent smoothness, where 


this is desirable and where high-frequency 
methods are elsewhere applied. Transmission 
systems of more nearly standard type may also 
be applied, however, thinking now of small 
selsyns and autosyns, especially where the com- 
puters produce mechanical rotations directly. 
Pneumatic transmissions have also been con- 
sidered, and would certainly be practical when 
this medium is employed in other parts of the 
system. One advantage is that no follower se- 
quence is required. Pressure in a closed system 
may be carried to a remote point for deflection 
purposes with considerable guarantee of ac- 
curacy, speed, and lack of hysteresis, provided 
that the appropriate newer techniques are ap- 
plied. 

4 THE QUESTION OF 

ROLL STABILIZATION 

The general method, used by us in the PUSS 
system, of splitting the computation and manip- 
ulation into two components corresponding 
separately to azimuth and elevation, these co- 
ordinates being referred to from the pilot’s 
point of view, has several consequences in dy- 
namic performance which compare unfavorably 
with the circumstances of a single-gyro de- 
flected sight. It is evident, thus, that when the 
airplane is rolled instantaneously, this having 
obviously no effecU on the trajectory of the 
projectile, the sight line will initially be moved 
in space in a direction and speed depending on 
the lead angle, measured from the axis of roll, 
and on the rolling maneuver as such. While this 
occurrence is only transient and will disappear 
in the steadier conditions which should pre- 
sumably precede the firing instant, the response 
of the line of sight in this manner to roll may 
enter the tracking dynamics and influence the 
stability thereof. One possibility is that it may 
affect skid, although one does not know whether 
beneficially or harmfully, and such questions 
are important enough to be studied before flight 
tests are made. Flight tests on analogous struc- 
tures give reason to believe that this problem 

^Aside, for example from centrifugal effects owing 
to the displacement of the projectile from the roll 
axis. These are probably small in practice. We have 
postulated only a hypothetical circumstance, not di- 
rectly related to actual events. 


* 1 ^ FIDENTIAlJ 


COMPONENTS AND SYSTEMS 


153 


may not be serious, however, but we should not 
like to let a large development program depend 
on such tenuous data. One usage to which it 
has been hoped that the electronic tracking 
simulator might be put was to just such ques- 
tions of dynamic stability as this, where the 
human response is involved. The reader is re- 
ferred to Chapter 2 for a discussion, on a more 
general plane, of the analytic and synthetic 
possibilities in connection with this type of 
question. 

In any case we now know that this roll tran- 
sient, whether adverse or otherwise, can be 
compensated for quite completely by relatively 
simple means. We say relatively since it is quite 
evident that a straightforward although cum- 
bersome measure for its elimination would be 
to roll stabilize the whole sight head, for ex- 
ample, or the whole system, allowing no rota- 
tion in space about the roll axis. It is only 
necessary to employ an angular rate meter meas- 
uring the roll rate, or an angular accelerometer 
measuring its acceleration, and form the ap- 
propriate^ dynamic connection to prevent 
transient turning of the line of sight. It is now 
felt that this problem, if it indeed arises in 
serious proportions, will not long remain un- 
solved in a practical sense. 

On a somewhat higher plane it may be re- 
iterated here that all the functions of free gyros 
and stabilization equipment may be duplicated 
by a system fundamentally including a set of 
three absolute angular rate meters (see Chapter 
3) fixedly disposed in the vehicle. 


COMPONENTS AND SYSTEMS 

Between the various inputs and the output 
aiming deflections, the computing portion of 
PUSS may be roughly segregated into a dy- 
namic computer and a static computer, each 
possessing several subsidiary components, and 
each being joined functionally to the other at 
a number of points. The dynamic computer em- 
bodies an operational connection, between one 
component w of angular rate and a correspond- 

^Suggested as a technique by the present writer, and 
given analytic form and justification by M. Golomb 
at The Franklin Institute. 


ing component A of angular sight deflection of 
the form 

^ B • T (a + A) , (1) 

in which A, B, and T are outputs of the static 
computers, and are slowly varying with time, 
at least in comparison with w and A. If one 
prefers it, the differential equation equivalent 
to the above operational equation is 

small 

+ o> + A +l+k—- (2) 

dt T T dt 

When A and B are made zero, this characteri- 
zation in either form will be recognized as that 
for a standard disturbed gunsight. Again if the 
time-parameter T is made infinite, the equiva- 
lent of a moving sight which is coupled to a free 
gyro is obtained, whereby, for example, a col- 
lision-course approach might be governed as 
explained in another place (see Chapter 1 and 
Chapter 8) . It is evident that the characteristic 
of the dynamic computer is essentially that of 
a first-order lag, as it may logically be called, 
with an adjustable lagging parameter coupled 
also to a sensitivity adjustment, and with addi- 
tive terms imposed on the input and output. 
There are many means for mechanization of 
such a characteristic. Those chosen thus far 
for the PUSS system have been resistance- 
capacitance filters, one synthetically produced 
in the electric or electronic version, and one 
obtained directly by pneumatic components in 
the pneumatic version. 

Figure 1 shows one schematic arrangement 
of the computation as employed in PUSS, which 
has had numerous variants, however, depend- 
ing on precisely which are applied of the vari- 
ous alternative input components which have 
been in development. No attempt is made in 
this figure to show in any detail the switching 
arrangements, for example, by means of which 
the operator may select at will the type of 
weapon for which solution is intended. These 
important technical features have been very 
completely described^-^ in reports to which 
reference is also made below, and it must here 
be pointed out that this entire development is 
still in progress, although it is now a closed 


]54 


INTEGRATED EQUIPMENT FOR THE PILOT 


to 

H 

3 

0. 



c/> 

K 

3 

a. 

K 

3 

o 


PUSS 

INCLUDING PACT 

Figure 1. Schematic diagram of PUSS system; AFCS Mark 4; Project N()-26r). 


rom<ll)KNTIAi. ' 




COMPONENTS AND SYSTEMS 


155 


issue as far as the direct responsibility of 
NDRC Section 7.2, as such, is concerned. 

To name the automatic inputs of PUSS in 
one of its most likely forms, we may list basic- 
ally : static and dynamic air pressures, vertical 
acceleration, temperature, and the two absolute 
angular rates of the vehicle. Certain implicit 
inputs relate to the characteristic of the air- 
plane itself, and are made on installation. Only 
one manual input must be made during opera- 
tion, however, aside from the choice of weapon, 
and assuming of course that appropriate auto- 
matic means is worked out to synthesize the 
temperature of the rocket propellant, and that 
one is target altitude. Even this is unnecessary 
if, with a different basic set of inputs, auto- 
matic radar range or radar (FM or pulsed) 
altitude is provided as is being considered. To 
continue with the inputs named, the angular 
rate inputs would be handled in dynamic com- 
puters of the type for which equation (1) is 
definitive, one channel^ each for azimuth and 
elevation. In the azimuth channel it may be as- 
sumed that the “secular” parameters A and B 
are absent, and further the time-parameter T, 
although simultaneously set into the dynamic 
computer of both azimuth and elevation chan- 
nels, is multiplied by a constant ratio in the one 
as compared with the other. This is a stratagem 
whereby the correction for gravity can be ef- 
fectively made in the proper direction, in the 
presence of uniform bank, in spite of its explicit 
treatment in the elevation component alone.^ It 
remains to describe, for this same set of inputs, 
how the parameters A, B, and T are computed, 
and then to describe the interconnected com- 
puter (PACT) for toss bombing. 

As intermediate steps in the computation, 
certain implicit variables are first obtained. 
Thus glide angle is obtained in terms of the 
static pressure and the dynamic pressure, in the 
process of which a differentiation of a function 
of static pressure is performed, it being evident 
for example that the glide angle y may be de- 
rived in terms of true airspeed, itself a function 

'‘Note, however, the remarks in an above section on 
the possibilities of roll stabilization. See also the bib- 
liography. 

‘This technique is believed novel in PUSS, and was 
conjured up by M. Golomb, mathematician to the 
project. 


of indicated airspeed Vai and altitude h, and 
the rate of change of altitude, the altitude itself 
being (again) expressible in terms of the static 
pressure. It is probably not necessary to men- 
tion that indicated airspeed is measurable in 
terms of the difference between the dynamic 
and the static pressures. Range R to the target, 
of course on a relatively straight approach, is 
calculable, as an intermediate or implicit vari- 
able of the computation, directly from altitude 
and glide angle. Then the angular rate param- 
eter A, and the lead parameter B are themselves 
obtainable from the quantities now available. 
The parameter A is derived as A(y), or as a 
function of glide alone; while B is given by 
B iy >Vai,®), and as a function of glide, indi- 
cated airspeed, and temperature is the most 
complex item. The time-parameter T is com- 
puted as T(^) , a function of range alone. These 
latter computations take place principally 
through multiple linkages, which were designed 
directly from graphical representations of the 
form the respective functions must have for 
accurate results of fire. In Chapter 5 this 
general philosophy was more fully treated. The 
computation for rockets and bullets, in one 
variant of PUSS, has now been traced through. 
We shall return again to a consideration of 
various questions with regard to certain indi- 
vidual components. But first we shall explain 
the operation of the PACT toss bombing 
computer which is involved, thus far, only as 
a component of the pneumatic version of PUSS. 
It was felt that an electric mechanization of 
the toss bombing (or toss rocketry) functions 
would too closely duplicate other BuOrd ac- 
tivity, notably that at Bureau of Standards. 

The inputs for PACT are the dynamic and 
static pressures and the vertical acceleration as 
measured by a captive-mass accelerometer. 
Again a manual input of target altitude must be 
made, but this input is common both to PACT 
and the rest of PUSS, as are the static and 
dynamic pressures. The static pressure, as a 
function of altitude, is utilized through the mo- 
tion of an aneroid capsule, together with the 
motion of a differential meter responding, as a 
function of indicated airspeed, to the difference 
between the static and dynamic pressures, to 
develop an auxiliary variable as the output of a 


CONFIDENTIAL 


156 


INTEGRATED EQUIPMENT FOR THE PILOT 


portion of the PACT computing linkage. In a 
pneumatic force-balance accelerometer, a pres- 
sure corresponding to the vertical acceleration, 
adjustably lagged, is made to provide a me- 
chanical motion, along with the auxiliary varia- 
ble above mentioned, continuously to compute 
the velocity a bomb must have, in the direction 
upwardly normal to the direction toward the 
target, sufficiently to counteract gravity. On the 
pull-up, in the toss bombing tactic, action of a 
pneumatic integrator is initiated which com- 
putes, via the integral of the increase in total 
vertical acceleration of the airplane, the corre- 
sponding normal velocity being thereby im- 
parted to the bomb. When these two computed 
variables are equal, as indicated by coincidence 
of output linkage rotations, the projectile is 
automatically released. In PUSS, the inputs and 
computing components of PACT are, at least 
in the preliminary model, physically inter- 
spersed and interwoven with those of the re- 
mainder of the system. All this has taken place 
according to Pollard’s theory of toss bombing, 
as also has the following arrangement for spe- 
cial settings in the dynamic computer of PUSS 
during the operation of PACT. In toss bombing 
operations ki order to follow an initial approach 
which allows for target motion, the elevation 
sight deflection is made zero,^ the time param- 
eter T is set at maximum, or approximately at 
20 seconds, and the parameters A and B are set 
to zero. Simultaneously the “flxed” parameter 
ky the constant of coupling as shown in Figure 
1, is set at the value 2 rather than about 1.2, as 
it is for the other aiming functions. 

The heart of the PUSS system proper, 
namely the dynamic computing component, is 
fed principally by the directly measured abso- 
lute angular rates. In early forms of PUSS, the 
functions of the present gyro inputs and dy- 
namic computers were accomplished by other 
means, and such other means were the subject 

^Or rather, the sight reticle is aligned, in elevation, 
with a definable fixed axis in the airplane, along 
which also the vertical accelerometer does not de- 
tect. Allowance for target motion in elevation is a 
consequence, discussed elsewhere in this report, and 
also in the writings of H. Pollard (of AMG-C), of the 
influence of curvature of the flight path on the ver- 
tical acceleration itself. This latter phenomenon is 
similar to an analogous one in rocketry computers. In 
both cases the method works only near certain average 
glide angles. 


of much investigation. Proposed systems ranged 
all the way from the now standard dome-type 
eddy-current gyro systems to those with sepa- 
rate precessing motors similar to gunsights 
developed, as has recently come to light, by 
Zeiss for the GAF. A variety of special linkages 
and servo systems were considered for such 
systems, all of which involved only a single 
gyro. We have discoursed, in Chapter 3, on the 
advantages claimed, particularly in flexibility 
for new functions, for the present technique of 
operating on a fundamental direct measure- 
ment of angular rate by whatever dynamic 
characteristic is appropriate to the occasion. In 
particular the way to higher performance is 
thus opened through the application of higher- 
order dynamics. We have discussed also, in 
Chapter 3, the captive gyro developments which 
have been carried out for the angular rate in- 
puts to PUSS, including the pneumatic and 
capacitative one-dimensional units, and the 
two-dimensional current servo case. Certain 
phases of this research are still under way, but 
progress and future promise is evident on all 
the types named. 

In the measurement of glide, the pneumatic 
version of PUSS depends at present on a mea- 
surement of the rate of change of barometric 
pressure, which together with that pressure 
itself, and indicated airspeed, gives the glide 
angle, and consequently also the range, by a 
solution equivalent to that of the obvious tri- 
angle. Some research has been conducted on a 
refined type of differentiator, involving feed- 
back, which is still in development. The stand- 
ard rate-of-climb instrument is somewhat in- 
adequate for this task. An analogous solution 
to the problem of the provision of glide, is now 
planned for the first electric version of PUSS. 
Here an existing component, employed in the 
so-called glide bombing attachment [GBA] , for 
the bombsight Mark 15, has been modified for 
this purpose. By following the motion of an 
aneroid diaphragm system, having a static 
pressure connection, through a mechanical in- 
tegrator disk, both altitude and its rate of 
change are developed as shaft rotations. Hence, 
with airspeed, glide may be derived again as 
above. A competitive method for measuring 
the glide, in this case 8, as has been employed in 
several other systems, is by detection of one of 


i 


OXFIDENTIAL 


COMMENTS ON PNEUMATIC COMPONENTS 


157 


the gimbal deflections in a gyro horizon. One 
objection to most such instruments, however, is 
that they will ‘‘spill” at certain extreme bank 
or dive angles. This is not the case, or at least 
very rarely so, with the new Sperry altitude 
gyro, nor, it is understood, with a Pioneer 
horizon now in development. Here, however, the 
measurement of gimbal rotation is made diffi- 
cult since it is the inner gimbal which is in- 
volved. A method of capacitor measurement can 
solve this problem, it has been decided, and may 
be appropriate if such measuring methods are 
elsewhere employed. An experimental assembly 
is now in preparation, involving a pair of radial 
plates, rotating relatively with the desired (but 
mechanically remote) gimbal motion, in series 
with a larger and constant capacitor acting as 
slip ring. No friction load need thus be added, 
and known methods of capacitance measure- 
ment may be directly applicable. We may men- 
tion briefly still other methods which have been 
considered for the effective and continuous de- 
termination of the glide. In PUSS, the acceler- 
ometer method, giving the cosine of glide (8) 
under conditions of straight flight, is not ap- 
propriate on the one hand, since the error due 
to target motion and path curvature does not 
necessarily correct for the target motion, as in 
other cases, but on the other hand such errors 
might here be removed since angular rate of 
the airplane about its lateral axis is continually 
measured as an input. A question of stability 
in tracking still arises, however, and it has 
been less troublesome to apply other techniques. 
Still another possibility, instrumentally unex- 
plored, is to employ the longitudinal component 
of total acceleration, as a measurement of glide, 
since it is unresponsive to curvature of path. 
Correction for the rate of change of true air- 
speed would there be required. 

Certain altogether different approaches to 
the PUSS problem have been proposed, and as 
yet only partially explored.^ 

‘‘There is the proposal of R. 0. Yavne (see bibliog- 
raphy) to mechanize the firing solution with a system 
equivalent to a free-gyro sight, however embodied, in 
which the coupling constants (such as the above) are 
varied with range, for example, or time. It is not im- 
possible that such an arrangement might ultimately 
prove to be superior, and exploration of such alterna- 
tives should continue as long as there is judged to be 
a need for PUSS as such. 


From a more practical standpoint, we may 
mention the question of installation. In this 
connection it has been proposed by BuOrd that 
the PUSS computer, whether pneumatic or 
electric, be contained in a wing tank with re- 
mote connections to the pilot-operated controls 
and to the sight head (see above) . At least for 
experimental work, and possibly further, this 
may have certain nonignorable advantages. 
Note that such radar systems to be employed as 
potential inputs to PUSS, in particular for the 
range itself, will be somewhat similarly in- 
stalled in any case. It is evident that the re- 
moval and reinstallation of computers, for 
calibration or for several experimental pur- 
poses would thereby be greatly aided. Further, 
this would allow a separate and local pilot in- 
stallation, for dynamic and static pressures, 
which permits engineering of these inputs to 
suit special needs better than ordinarily do the 
standard equipments available in airplanes for 
flight purposes. It is now planned to make such 
installation, with the preliminary models of 
PUSS at least. Certainly even the smallest drop- 
pable auxiliary gas tank should provide ade- 
quate space. 

This is perhaps an appropriate place to men- 
tion that the current experimental PUSS 
model, soon to be prepared for tests, has been 
officially designated aircraft fire control system 
[AFCS] Mark 4. 

10 6 COMMENTS ON PNEUMATIC 
COMPONENTS 

In Chapter 3 of the present report, we have 
discussed the properties of captive gyros, in 
particular of the pneumatic variety. The pneu- 
matically captured gyros, employed experimen- 
tally for PUSS and for otheU systems, have all 
been of the one-dimensional type, measuring 
absolute angular rate of a framework about 
one axis fixed therein. These developments have 
been the work principally of NDRC Section 7.3. 
In the pneumatic version of PUSS, two such 
captive gyros are contemplated for the angular 
rate inputs, and a third — forming, thus, a 
symmetrical set — might be included for more 

iFor example in BARB, as embodied in bombsights 
Mark 23 and 27, and for aircraft camera stabilization. 


158 


INTEGRATED EQUIPMENT FOR THE PILOT 


general, or more universal, types of aiming 
control. Components are now available for test- 
ing, both separately and in combination with 
the other components of the system. 

As we have said, pneumatic force-balance 
components are being applied for the determi- 
nation of rate of climb and for the integration 
of incremental accelerations, the latter varia- 
bles themselves being determined by similar 
means. For such applications the pneumatic 
medium leads, at least potentially, to very 
smooth and rapid operation, and to lightness 
and compactness of design. For dynamic com- 
putations, connected systems of rigid tanks and 
capillary tubes are usable in a manner similar 
to electrical resistance and capacitance, and 
analogous feedback techniques apply where 
nonpassive systems must be synthesized. In 
such cases, however, certain restrictions must 
be observed to obtain predictable or linear per- 
formance, for example. Typically, the time 
parameters of such networks are generally pro- 
portional to the absolute pressure in their com- 
ponent elements, so that either compensation 
must be included for such effects or the varia- 
tions in pressure (as in orthodox acoustic 
theory, for example) must be kept small in com- 
parison with the absolute level. Furthermore 
condensation and leakage must naturally be 
rigidly guarded against, although techniques 
are known which may insure safety from such 
deleterious influences. (See Chapters 3 and 4 
of Volume 1, Division 7.) 

The purposeful variation of parameters, in 
dynamic computers of the pneumatic type, may 
be accomplished by several means. If continu- 
ously made (during normal operation, that is) 
the obvious mechanical method of varying 
pneumatic capacitance by changing the volume 
of tanks seldom gives the desired result since 
a “forcing function’^ is imposed on the pres- 
sures in the system, continually altering thus 
the initial conditions, so to speak. Adjustment 
of pneumatic resistance is more appropriate, 
since the storage of energy is not involved 
there, and the techniques of so doing are cen- 
trally important in this art. Needle valves are 
prone to many failings, from a practical as well 
as theoretical standpoint. Step adjustments of 
capillary tubing lead typically to much equip- 


ment and to concern over the continuity of 
overall operation. Under the express urges of 
the present writer, an ingenious and appropri- 
ate component for the variation of pneumatic 
resistance was devised for this application.™ 
The solution, now experimentally embodied in 
components for pneumatic PUSS, involved a 
stack of thin punched disks, with alternating 
types of hole, whereby a labyrinth resembling 
capillary resistance was adjustable in effective 
length as imposed between the terminal con- 
nections. An easy mechanical adjustment was 
permitted. For details we refer again to reports 
of Section 7.3. 

For shifting operations, whereby the pneu- 
matic computer and allied equipment could be 
adapted rapidly and at will to the different 
functions desired of them, small solenoid-oper- 
ated valves of special type were developed. The 
entire pneumatic assembly is to be contained 
in a supercharged space, possibly later with 
complete recirculation of air (or w^hatever gas 
is employed). Regulated supply pressures, by 
means of pumps and feedback pressure-regu- 
lators, have been designed for and are expected 
to perform valiantly. The only possible objec- 
tion to the pneumatic version, of PUSS or of 
similar equipment, appears to be the unfamil- 
iarity of maintenance procedures. This is a con- 
troversial point, however, and appears less im- 
portant anyhow from the longer-term view- 
point. 

7 the CAPACITOR IN INSTRUMENTAL 
TECHNIQUES 

The application of continuous measurement 
of electrical capacitance in components of aim- 
ing-control systems has been referred to at sev- 
eral points. For the measurement of small 
mechanical motion, either for repetition in 
other physical variables or for the detection of 
error in a follow-up, it has numerous advan- 
tages. It can compete with photoelectric meth- 
ods as concerns the absence of “detent,” or of 
interference with the physical system under 
detection. But further and perhaps more sig- 
niflcantly, precision measurement may be car- 

“‘By J. F. Taplin of Section 7.3 (and Lawrance 
Aeronautical Corporation). 



PATHS FOR CONTINUING RESEARCH 


159 


ried out without the need for following agencies 
placed locally where the primary measured 
variable occurs. Thus, very small capacitors 
may be located in otherwise almost inaccessible 
spots, and their capacitance, in response to the 
primary variation with which they are asso- 
ciated, may be reproduced remotely in any de- 
sired tangible form. The possibility of employ- 
ing capacitative “slip rings,'’ in series with the 
measuring capacitor, as already referred to, 
permits electrical extraction of such measure- 
ments from mechanically complex systems, 
where otherwise direct conduction, with its at- 
tendant problems, would be required. 

To derive any reasonable function of a rota- 
tion, capacitatively, it is necessary only to shape 
the plates — or the dielectric — of the measur- 
ing capacitor in appropriate fashion. Employ- 
ing the electric laws of series and parallel 
capacitance, numerous elementary mathemati- 
cal operations, such as addition, may be per- 
formed from mechanical motions in a computer. 
For these applications, of course, a stable os- 
cillator must be provided. Frequencies of one 
megacycle appear to give satisfactory results 
in typical instances, whereas much higher and 
much lower frequencies have been successfully 
applied. It is naturally most efficient to resort 
to capacitor techniques where many of the op- 
erations in a system may thus be carried out, 
and where electronic channels are performing 
other functions, as well, of computation or 
manipulation. The combination, however, of 
such techniques with mechanical ones is sig- 
nificant, where for example the final motion of 
complex but miniature linkage computers may 
be extracted without load on the inputs or 
bearings, and where the size of the computing 
unit itself is not thereby appreciably increased. 

Information on the practicality of electrical 
capacitative methods for such applications 
should soon be available, since at least two such 
components for PUSS are now in development. 
Following rigorous tests in the laboratory, 
flight testing under conditions properly ar- 
ranged should simulate those of the final ap- 
plication at hand. Since such methods have been 
used in industrial and other systems for a long 
period, there is little reason for suspecting that 
they are inapplicable here. 


10.8 paths FOR CONTINUING RESEARCH 

One modification of PUSS not already men- 
tioned is that which has been suggested from 
several sources, and consists in what amounts 
substantially to presetting the gravity drop and 
other nonkinematic parts of the aiming cor- 
rection by a computation different from that 
executed by the dynamic process which is 
fundamental to the principle of the current 
PUSS method. We refer chiefly to the solution 
for rocketry. Such a modification might cer- 
tainly lead to a more rapid subsidence to the 
firing conditions, and in any case would pro- 
vide at least an approximate aiming correction 
if there were no time even for the brief track- 
ing interval which the PUSS method demands. 
It may be possible, at the longer ranges, to 
arrange for such presetting automatically by 
redesign of the linkage computers which are 
now contemplated. 

It goes without saying that many of the con- 
jectural schemes for aiming control which have 
been mentioned throughout this report may well 
deserve further study, and it would hardly be 
surprising if some of them proved revolution- 
ary in the increased powers of fire control 
which they might allow. For the future, cer- 
tainly, there is more time for such theoretical 
or basic study, and the newer techniques may 
arise either out of mathematical or instru- 
mental advances in thinking, or again purely 
empirically from quantitative study of the 
physical sections of the problem. It would 
naturally be folly to work without recognition 
of the probable forms of future weapons, but 
the recommendation of the present writer 
would be to treat projectiles from a rather gen- 
eralized point of view, so that rather than be- 
ing outmoded, the theories and systems to be 
developed may simply be adapted by the fixing 
of parameters in the control and computational 
components. 

One may look somewhat beyond the immedi- 
ate objectives of PUSS, and without, indeed, 
losing sight of them, consider some of the 
logical extensions which should ultimately be 
attainable. We mention these although thereby 
we actually pass into somewhat different 
branches of ordnance (see Chapter 8) . More or 
less automatically, PUSS will be associated with 


CONFIDENTIAL ^ 


160 


INTEGRATED EQUIPMENT FOR THE PILOT 


the jet-propelled airplane types, and this has 
certain significance to our final point. 

In somewhat earlier discussions" it was con- 
templated what might ensue if the fighter plane 
were to be equipped with an automatic pilot of 
really high performance. As a generalization of 
PUSS, suppose that the pilot, in attacking a 
target wherever located, were simply to em- 
ploy a stabilized sighting system, carried in his 
fighter, to track the target through the manip- 
ulation of controls which operate the line of 
sight through optimum dynamics, and do not 
primarily have to do with flying his vehicle. 
With the direction to the target thus well estab- 
lished, and the special properties of this direc- 
tion continuously determinable, a computing 
component would develop, in continuous man- 
ner also, the direction of flight necessary for 
successful fire. This latter direction, by in- 
structions from the computing system to the 
high-performance automatic pilot, would be 
undertaken by the airplane. Thus we have what 

"With Commander E. S. Gwathmey of BuOrd. 


amounts to a director for fighters. While there 
are many details to be filled in, there is nothing 
really insuperable about the problems of such 
a system. 

Further, it is evident that with the pilot’s 
task reduced to that of tracking the target, he 
may be replaced by an automatic follower which 
“locks on” the direction to the target by the 
available radiated or reflected data therefrom. 
The vehicle, without human passengers, is now 
unlimited as to violence of maneuver, for ex- 
ample. As one important special case, which 
incidentally may be resorted to if desired with 
PUSS in its present form, the vehicle itself as 
projectile may be steered on an interception 
course with the target. Here, then, we enter 
into the field of guided missiles. The techniques 
of the two fields are not widely separate, in fact, 
even at present. Each has much to learn from 
the other, in apparatus and in developmental 
procedures; and for the newer weapons — if 
such there must be — can best proceed in the 
fullest kind of cooperation and understanding. 


^ y'ONFIDE?sTIA: 


PART II 


AERIAL TORPEDO DIRECTORS 




lONFIDENTIAL 


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•* 


PREFATORY COMMENTS 


A ircraft torpedo director developments under 
^ Section 7.2 of NDRC were carried out at The 
Franklin Institute as part of Contract OEMsr- 
330. G. A. Philbrick was responsible for the 
earlier work, which he has described in Part I. 
Since the spring of 1943 these developments 
have been under the cognizance of the present 
writer, but with much helpful collaboration from 
Mr. Philbrick. The transition from one super- 
visor to the other was somewhat gradual, with 
no sharp dividing line. Consequently, it has not 
been practical for Mr. Philbrick and the present 
writer to prepare two reports, each covering 
distinct phases of the development work. Mr. 
Philbrick has described a part of the aircraft 
torpedo director work, and this report is in- 
tended to complete his descriptions and to add 
descriptions of the remainder of the work in 
this field. 

For complete detailed descriptions of the 
various directors developed, the reader is re- 
ferred to The Franklin Institute reports listed 
in the Bibliography. 

Several ideas that never reached the develop- 
ment stage might warrant a word or two. Some 
thr ^ht was given to a so-called rule-of-thumb 
method of aiming torpedoes.^^ This consists in 
the pilot aiming a predetermined number of ap- 
parent ship lengths ahead of the target. The 
trouble is that analysis shows that for even 
moderate accuracy the predetermined number 
referred to must come out of a fairly large and 
complicated table which the pilot must mem- 
orize. Opinions differed widely as to the value 
of the method. 

Further work on the apparent length method 
was done in applying it to the technique of toss- 
ing torpedoes.^^ The suggestion was to toss a 


torpedo like a toss bomb, but aimed to hit the 
water about 200 yards (the arming distance) 
in front of the target. A modified toss bomb- 
sight was used for this purpose, and the Navy 
asked Section 7.2 for an analysis on what lead 
angles to use. Opinions differed on the value 
of using an expensive torpedo for a toss bomb. 
Tests indicated that sufficient accuracy to make 
it worth while was not obtained. 

At one time the Bureau of Ordnance sug- 
gested making a torpedo director for dropping 
gyro-angling torpedoes. Section 7.2 did not have 
much enthusiasm for this development and did 
not undertake it. If an attack is made by aiming 
the plane at the target (either with zero lead 
or on a collision course), relying on the gyro 
angle setting to provide the lead by causing the 
torpedo to turn in the water, a no-deflection shot 
is given to the antiaircraft gunner on the target 
ship. If the gyro angle setting on the torpedo 
is used to permit the pilot to attack so as to 
minimize the danger from AA fire, a large lead 
angle must be employed, and that increases the 
difficulty in sighting through the director op- 
tics. It appeared that a zero gyro angle (or 
straight) shot represented the best compromise 
between the two difficulties, and it certainly 
resulted in a simpler director. Eventually the 
Navy abandoned the idea. 

One development that might be called one 
of the odds and ends was the computer for a 
torpedo director trainer.^® This was to calculate 
and show the error in hitting while using the 
standard trainer for the torpedo director Mark 
30. The computer was 90 per cent complete when 
stopped at the end of the war. 

A. L. Ruiz 


CONFIDENTIAL 


1 


163 




Chapter 11 


COURSE STABILIZATION 


TN THE SOLUTION of the aircraft torpedo at- 
^ tack problem it is necessary to know the 
target course and speed. These quantities could 
be measured if a suitable tracking mechanism 
were installed in the attacking plane to deter- 
mine target bearing and range over a period 
of time and to feed that information into a 
computer. The amount of mechanism involved, 
however, would be fairly large and the use of 
an additional operator would be required. In 
order, therefore, to avoid such undue complica- 
tion and weight, aircraft torpedo directors have 
been built on the assumption that the course 
and speed could be estimated with sufl5cient 
accuracy. 

Normally, instead of target course, it is much 
easier to estimate target angle (or “angle on 
the bow”). In effect, this is the orientation of 
the target with respect to the line of sight, and 
is, therefore, the angle seen by the pilot as he 
looks at the target. From the target angle, own- 
plane course, and the relative target bearing, 
target course may be computed (Figure 1). 
But it is not necessary to make this computa- 
tion since the target angle can be used in solv- 
ing the attack problem (Figures 2 and 3). 

Ht 


target 



TARGET'S DiRECTlOH OF MOTiO** 



Figure 1. Han view (rf target and own (attacking) plane. 


Inasmuch as the target angle is a function of 
the target course, own-plane course, and rela- 
tive target bearing, it is apparent that the 
target angle changes as the attack progresses 


TARGET AT TIME 
OF FIRING 



Figxtre 2. Plan view of torpedo firing problem. 


and the plane approaches the target (Figure 
4). Thus, if the pilot estimates and sets target 
angle early in the approach his setting will be 
wrong at the time of attack. Hence the pilot 
must make a last-minute adjustment and es- 
timate of the target angle before releasing his 
torpedo. With the numerous other things that 
he has to do at the moment of release this is an 
additional burden of which it would be well to 
relieve him. 

A method has been suggested* for relieving 
the pilot of this last-minute estimate of target 
angle. The torpedo attack problem can be 
equall}’ well solved by using track angle instead 
of target angle (Figures 2 and 3) . From Figure 
4 it is apparent that track angle is the supple- 
ment of the angle between the target course 
and own-plane course. To determine this angle 
directly, a miniature ship model is located on 
the end of a shaft convenient to the pilot. The 
pilot may turn this ship model until it lies 
parallel to the target’s direction of motion as it 

•By Lieutenant Freeman of the Bureau of Aero- 
nautics. 



165 



]66 


COURSE STABILIZATION 


appears to him. Momentarily then, the angle 
between this ship model and the plane's fore- 
and-aft axis would be the track angle if the 
plane were on a proper course for release. To 
keep this angle correct after it is once set, the 
ship model is clutched in to a directional gyro- 
scope so that regardless of the plane's changes 
of direction the ship model will remain parallel 
to its original setting. Thus, as long as the 
target does not change course the torpedo 
director has available a continuous setting of 
the difference between target's course and 
plane's course. At any time that the plane is 
turned so as to be on a correct torpedo firing 
course by putting the director's cross wire on 
the target, this difference represents the cor- 



Figure 3. Plan view of torpedo firing problem; same as 
Figure 2 with all sides of triangle divided by time of run. 

rect track angle. Consequently, the pilot may 
make his target course setting early in the ap- 
proach and is relieved of the necessity of mak- 
ing a last minute adjustment before release. 

Use of a directional gyro and the principle of 
course stabilization was first made in the tor- 
pedo director Mark 32.^^ As a result of tests on 


this director both the Army and the Navy re- 
quested the modification of a torpedo director 
Mark 30 to add a directional gyro and a ship 
model for stabilized target course.^® Tests on 


OWN PLANE 



both of these at Fort Lauderdale and at Eglin 
Field were very gratifying. All pilots who used 
the director were well pleased with the course 
stabilization feature. As a consequence of the 
Eglin Field tests the Army requested the devel- 
opment of a new torpedo director utilizing a 
different set of optics. This was completed in 
June, 1944 and was adopted as standard by the 
Army and designated the torpedo director 
B-3.^1 A similar director with different optics 
combined with a low-level bombsight was built 
for the Navy at about the same time.^^ 


C ONFl 


lAi; 


Chapter 12 


PRESENT-RANGE TYPE TORPEDO DIRECTORS 


'X’HE TORPEDO DIRECTORS Mark 30 and 32 (and 
all earlier ones) were built to use an esti- 
mate of torpedo run as an input. The reasons 
for this were twofold: the solution for lead 
angle as a function of present range and other 
variables is implicit and transcendental; no 
simple mechanization had ever been found. Con- 
sequently it was simple to rationalize and con- 
vince oneself that it was just as easy to estimate 
torpedo run as present range. 

But the increasing use of radar in torpedo 
planes spurred on the search for a simple 


TARGET POSITION 
AT RELEASE 



present-range type of computer. At last the 
answer was found : it is described in Chapter 6. 

The trick consisted in locating a point on the 
torpedo path from which a fictitious torpedo, 
having a constant speed equal to the water 


speed of the real torpedo, could be launched in 
water at the same time the real torpedo is re- 
leased, and reach the target simultaneously 
with the real torpedo. Using this point it is 



Figure 2. Present-range solution, second step. 

Note. Point, from which a fictitious torpedo with a constant 
speed equal to that of the real torpedo starts in water at the 
time the real torpedo is released, and reaches the point of impact 
simultaneously with the real torpedo. 

possible to break the problem down into two 
parts: the first is a computation for the lead 
angle for the fictitious torpedo, and involves 
only the target speed, track angle, and torpedo 
water speed; the second is a correction com- 
puted from own-plane speed, present range, and 
time-of-fall (obtained from altitude by assum- 
ing a fall in vacuo tf = \/2H/g ) . 

The detailed stages in the solution are illus- 
trated in Figures 1 to 6 inclusive. Figure 6 is a 
schematic diagram of the linkage built. The unit 


ONFIDENTIA 


167 


168 


PRESENT-RANGE TYPE TORPEDO DIRECTORS 



length in triangle III is the base line, at one 
end of which is pivoted the link A (turned 
through the track angle by the pilot’s setting 
and the directional gyro), and at the other is 
the link B. The length of A is made equal to 
Vs/yt by a cam, and the ends of A and B slide 



V^T. 

Figure 4. Present-range solution, fourth step. 



together. In triangle IV the link C is fixed in 
length and equal to unity. One end of C slides 
in link B, and the other is moved along the base 
line by a series of logarithmic dials and an ex- 
ponential cam a distance equal to ( — Vt) tf/R. 
The lead angle jS is found in triangle IV and 
applied to the optical system. 

Two present-range types of director were 
built by modifying torpedo directors Mark 30, 
and were completed just as the war ended.^^ 



Figure 6. Present-range solution, sixth step. 



Chapter 13 


TORPEDO DIRECTORS FOR USE AGAINST EVADING TARGETS 


ALL TORPEDO DIRECTORS to date (and in fact 
^ all gun directors) have been designed for 
use against targets moving in a straight line 
with constant velocity. The arguments in favor 
of the constant velocity assumption were two- 
fold: 

1. Many targets were not dangerous unless 
moving in a straight line (e.g., a bomber had 
to make a straight-line approach) . 

2. Since no control over the missile was pos- 
sible after launching, a straight-line target mo- 
tion represented the most probable condition 
for prediction. 

These arguments were considerably weaker 
in the case of a torpedo-plane attack than for 
many other missiles. Upon observing the ap- 
proach of a number of torpedo planes, the 
target was likely to start turning in an effort 
to avoid being hit. With modern antiaircraft 
systems this turning would not materially les- 
sen the ability to put out a strong deterring fire 
against the torpedo planes. The attacking pilots 
were thus forced to estimate the correction to 



Figure 1. Error made by using straight-line prediction 
with turning target. 


be applied to their straight-line type of di- 
rector in order effectively to fire torpedoes at 
a turning target, and this correction could 
often be very large (Figure 1). In order to 
relieve them of the burden of making this 
estimate the development of a maneuvering 
type of torpedo director was undertaken. 



SPEED FROM HERE ON 
Figure 2. Kinematics of turning ship. 

The kinematics of a turning ship have been 
described in detail in various Navy publica- 
tions. Qualitatively the sequence of events fol- 
lowing the order to execute a turn may be 
described briefly as follows (Figure 2) : 

When the rudder is turned, the bow of the 
ship gradually begins to turn in the same di- 
rection. The ship, however, due to its momen- 
tum, continues to move in a straight line for 
an appreciable length of time, say 20 to 30 
seconds depending on the type of ship. At the 
end of this time interval it will be noticed that 
the ship has begun to change its course or di- 
rection of motion. The actual path of the ship 
then departs more and more from a straight 
line until the ship has turned approximately 
90 degrees, when its path of motion becomes a 
circle. During all this time the ship's speed has 
gradually reduced reaching a stable value after 
about a 90 degree turn. From that time on the 
ship continues to move in a circle at a constant 
velocity with its fore-and-aft axis pointed in- 
ward from the tangent to the circle. The di- 
ameter of the circle, the terminal speed of the 
ship, the amount of deviation of the ship head- 


|confidentIac ^ 


169 


170 


TORPEDO DIRECTORS FOR USE AGAINST EVADING TARGETS 


ing from its direction of motion and the char- 
acteristics of the transition to circular motion, 
all depend on the type of ship, its initial speed 
and the amount the rudder is turned. 

Early attempts at making a torpedo director 
effective against a maneuvering target con- 
sisted of arbitrarily reducing the target speed 
input to the director and altering by a fixed 
amount the target angle (Figure 3). The 


ARBITRARY ALTERATION 
TO TARGET ANGLE 



Figure 3. Illustrating early method for using straight- 
line prediction on turning target. 


amount of speed reduction and target angle 
alteration were chosen for a specific set of 
standard conditions. Any departure from these 
conditions during the attack caused errors 
which sometimes were more than the total 
lead angle. 

It was considered that a much better solu- 
tion was needed if the resulting director was to 
be of practical use. The Statistical Research 
Group [SRG] at Columbia University, operating 
under contract to the Applied Mathematics 
Panel, was asked to analyze the theoretical as- 
pects of the problem. The first attempt at a 
solution was to consider a squadron attack. 
Taking the turning characteristics of the USS 
Washington and assuming that all variables 
were known exactly, and that there was no 
dispersion in the missile, the SRG calculated 
the required number of torpedoes and their lead 
angles to insure at least one hit regardless of 


what the target should do after the launching 
of the torpedoes. It was contemplated that each 
attacking plane would be assigned a number 
which designated its position in the squadron 
and that this number would be one of the vari- 
ables set into the torpedo director. Each attack- 
ing plane then would have a different lead 
angle depending upon its position in the squad- 
ron. 

While the early work indicated that this 
method could be used, it was felt after consul- 
tation with the Bureau of Ordnance that re- 
liance should not be placed on coordinated at- 
tacks of this sort, since there was too much 
opportunity for materiel and personnel fail- 
ures. Instead it was felt that a director should 
be constructed that would permit the success- 
ful launching of a torpedo against a maneuver- 
ing target in such a way as to give the optimum 
chances of hitting for each plane in the attack. 
With this revised point of view a new analysis 
was undertaken by the SRG. The first step was 
to systematize the procedure for calculating lead 
angles in attacks on turning ships. Since the 
equations of motion of the ship were unknown, 
this lead-angle calculation was of necessity done 
by a semi-empirical method, but a procedure 
was worked out whereby the number of steps 
was reduced to a minimum and tabulated so 
that comptometer operators could grind out 
the answers. 

The next step was to pick the most rep- 
resentative types of maneuvering that a target 
might be expected to use. It was agreed with 
the Bureau of Ordnance that all work would be 
carried out using the turning characteristics of 
certain classes of American warships. It was 
felt that with the inadequate existing knowl- 
edge of the characteristics of enemy ships, this 
would probably be reasonably representative of 
the actual conditions, considering that in battle 
the number of factors that would be totally or 
partially unknown would more than outweigh 
any errors that might be made because of this 
assumption. Since the purpose of going into a 
turn would be for the target to do its utmost 
to avoid being hit, it was reasonable to assume 
that the turns to be considered would be at es- 
sentially maximum rudder angle. Consequently 
all calculations were made for a rudder angle 
of 30 degrees. 


[roNi7m-:NTiAij 


TORPEDO DIRECTORS FOR USE AGAINST EVADING TARGETS 


171 


Inasmuch as the characteristics of a ship 
just entering a turn are considerably different 
from those of a ship well into a turn, all turns 
were divided into two broad classes — developed 
and undeveloped. It was arbitrarily assumed 
that developed turns would be all those in which 
the ship’s heading had turned 10 degrees or 
more from its original direction, and undevel- 
oped turns would be all others. One further as- 
sumption was necessary. A ship observed doing 
20 knots in a developed turn might have started 
its turn at a speed of 25 knots, or might have 
started its turn at a speed of 30 knots, depend- 
ing on how long it had been turning. There 
was no way to distinguish between the two 
cases without knowing in detail the past his- 
tory of the target motion. Therefore, lead an- 
gles were calculated on the basis of an equal 
probability of the target having started its 
turn at either of the two speeds. (Check cal- 
culations were made on the basis of other 
probabilities such as 3/4 and 1/4 or 2/3 and 1/3 
instead of 1/2 and 1/2. The results were found 
to be not far different.) 

Having decided on the above assumptions 
and procedures, the SRG then proceeded to 
compute a series of tables of lead angles for 
various attack conditions and target speeds, 
for all target angles, and for three classes of 
ships namely, a battleship of the Washington 
class, a carrier of the Yorktown class and a 
light cruiser of the Philadelphia class. These 
lead angles were calculated so as to give the 
highest probability of hitting for the given con- 
ditions. With these tables it was possible to 
begin the work of mechanization. 

The problem of mechanization was rendered 
more difficult by the fact that no formulas ex- 
isted. It was necessary to devise a mechaniza- 
tion which would fit with sufficient accuracy the 
tables of data computed by SRG. It was con- 
sidered more important to have an accurate 
solution for the case of a developed turn than 
for an undeveloped turn. Therefore, the efforts 
were concentrated on the former. Many ap- 
proaches to a solution were possible. The fol- 
lowing were the important ones that were 
considered : 

1. To build a brand new mechanism which 
would solve the lead angles for curved target 
paths. This method would mean abandoning 


the results of all the development work that 
had been done for torpedo directors for straight- 
line target motions. Inasmuch as the final di- 
rector should, as a special case, compute lead 
angles for straight-line motions, it was felt 
desirable to use this type of director as a 
foundation. Consequently, although work was 
done on this method, principally by expanding 
the lead angle in a Fourier series, it stopped 
when it soon became apparent that the results 
were not leading to an obviously simple mech- 
anization. 

2. Another line of attack was to assume that 
a director existed that would accurately solve 
for the straight-line lead angle and to add to 
that another mechanism giving the correction 
for a curved path. This might have worked out 
satisfactorily if sufficient time and personnel 
had been available to continue the work to 
completion. However, the third approach 
showed more promise and it was decided to 
concentrate on it. 

3. Mechanisms already existed for solving 
the lead angle problem for a straight-line 
course, as stated above. The question was asked, 
is it possible to determine fictitious values of 
input variables to such a mechanism so the 
output lead angle may be correct for a curved- 
target course rather than for a straight course. 
If this could be done then the resulting tor- 
pedo director would consist of a straight-line 
type of computer with an auxiliary computer 
that would add corrections to certain of the 
inputs when it was observed that the target 
was actually turning. Examination of the tables 
of data soon showed that mathematically speak- 
ing it was always possible to determine a fic- 
titious value of target angle in such a way that, 
when used instead of the actual target angle in 
a straight-line type of computer, the resulting 
output would be the correct lead angle for a 
curved course (Figure 4). It was^^ also found 
that it was not possible under all circumstances 
to find a fictitious target speed that would ac- 
complish the same results. However, an appro- 
priately chosen fictitious speed together with a 
fictitious target angle could be used. (A special 
case of this last method was that described 
above as the first attempt to produce a curved- 
type fire director, that is, to reduce arbitrarily 
the target speed by a fixed amount and alter the 


CONFIDENTIAL / 


172 


TORPEDO DIRECTORS FOR USE AGAINST EVADING TARGETS 


COMPUTED IMPACT 
POINT 



Figure 4. Use of fictitious target angle with straight-line computer to give lead angle for turning ships. 


target angle by a fixed amount. However, in the 
special case the results were valid for only one 
set of input conditions, whereas this develop- 
ment contemplated giving an accurate director 
for all input conditions.) Consequently, work 
was carried on for the first and third of these 
possibilities. 

The early lines of attack consisted in expan- 
sion in Fourier series. Considerable effort was 
put into this to bring the coefficients into tract- 
able forms, but the results obtained were not 
simple when sufficient terms were used to give 
what was felt to be a reasonable accuracy. 
Consequently, this expansion method was aban- 
doned in favor of empirical curve fitting. 

One rather accurate solution was obtained 
utilizing both a fictitious target speed and a fic- 
titious target angle. But it was apparent that to 
build a director for such a solution would result 
in an exceedingly complicated mechanism with 


many problems to solve before it could be made 
to work satisfactorily. So nothing further was 
done on this. 

The major effort was then concentrated on 
finding a suitable mechanism to give a fictitious 
target angle to be used in a straight-line di- 
rector. The variables involved were as follows: 
T = target angle 
Vs = target speed 
Vt = fixed torpedo speed 
R — present range 
h = altitude 

Va = ground speed of launching plane 
S = type of target ship 
t' = fictitious target angle as the output 
(Other variables were eliminated as a result 
of the assumptions and simplifications made as 
described earlier.) 

It was found that the launching plane's alti- 
tude and ground speed could be combined in a 


TORPEDO DIRECTORS FOR USE AGAINST EVADING TARGETS 


173 


single variable which represented the difference 
between the horizontal projection of the air 
travel of the torpedo in yards and the water 
travel of that torpedo for a time equal to the 
time-of-fall. (This was labeled A, and was 
equal to \/2h/g {Va—Vt)- 

Two empirical formulas were derived using 
these variables to give a fictitious target angle. 
The first of these was the sum of arbitrary 
functions of certain linear combinations of the 
input parameters, as follows. 

r' = r - X + 197.1 - 0.0997? + 0.101(A - 291) 

+ F,{y;) + F,{S) , 

where x is defined by the equation 

Fi{x) = F 2 (r) + 200 - 0.1 (7? - A + 291); 

and all the F’s are empirical functions. 

The second was the product of an arbitrary 
function of the sum of some of the variables and 
an arbitrary function of the sum of the target 
angle and others of the variables, as follows: 

r' = 0.00047 • 

[4900 - 7? + 1.5 A - 607. + 7^2(^)] Fi{Q) 
where Q is defined by the equation 
Q = 67.3 + T + 0.035(A - 7?) - 7. + Fz{S) ; 

and all the F’s are empirical functions (not the 
same as those in the first formula). Both of 
these could be mechanized fairly simply. Since 
the second, however, gave appreciably less 
error in the overall result, it was decided to 
use this formula as the basis for the final 
mechanization.^^ 

Work was just starting on the actual con- 
struction of this director when it was termi- 
nated as a result of the end of the war. As 
stated earlier the efforts were concentrated on 
an accurate solution for developed turns. It had 
been hoped to find a simple addition to the 
mechanism which would give the answers for 
an undeveloped turn. This has not been carried 
through to completion. However, it is not felt 
to be worth while to spend too much time to 
find a solution or to permit much additional 
complication to take care of this case. There 
are too many unknown factors entering into 
the problem and too many guesses that the at- 
tacking pilot has to make to warrant excessive 
accuracy at the price of excessive complication. 


Had the director been completed its form 
and method of operation would have been sub- 
stantially as follows. 

In front of the pilot there would be an op- 
tical system, perhaps similar to that of the 
torpedo director Mark 30, through which the 
pilot would observe the target and which would 
lay off the proper lead angle. This lead angle 
would be received from a remote computer by 
means of a servomechanism. Adjacent to the 
pilot would be control knobs for the input 
variables. Before making the approach the 
pilot would set his anticipated ground speed 
and altitude of attack. He would also adjust 
the turn knob to indicate a straight-line course. 
On sighting the target, the pilot would enter his 
estimate of target speed and the target class. 
He then would set target angle so that the 
small model adjacent to the optical system 
would line itself up parallel to the actual tar- 
get. This model would then be clutched to a 
directional gyro so that once set it would retain 
its direction in space regardless of the plane’s 
maneuvers, and thus always remain parallel 
to the target until the target should change 
course. As soon as it was observed that the 
target was in a turn rather than on a straight 
course, the turn control would be set to indi- 
cate a clockwise or counterclockwise turn. 

The pilot would then grasp the target angle 
rate-knob (which would be mounted concentric 
with the target angle knob) and adjust it so 
that the ship model would turn at a rate equal to 
the target’s turn. Thus the target angle would be 
continuously changing at the right speed and 
would keep set properly, allowing the pilot to 
concentrate on last-minute details of getting 
into proper position to launch his torpedo. 

If the director received range automatically 
from a radar, the pilot might drop the torpedo 
at any time he desired. If the range were set 
manually, the pilot would have set the desired 
dropping range early in the attack and would 
launch his torpedo when his plane reached that 
range. 

As soon as the torpedo was launched, the 
pilot would turn sufficiently from his course so 
as to avoid as far as possible the target’s anti- 
aircraft fire and get his plane sufficiently far 
from the target to get him away from the blast 
of his torpedo as it hits. 


[cot 


CONFIDENTIAL 







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PART III 


AERIAL GUNNERY 


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PREFATORY COMMENTS 


T his report gives a summary of the field of 
aerial gunnery, and particularly that part 
of the field with which Section 7.2 of NDRC 
was primarily concerned. During World War II, 
by far the largest part of the development 
work in this field was on flexible gun systems 
for bomber defense so that very little is said in 
this report about fixed gun systems. This is not 
intended to imply that fixed gun systems are 
less important than flexible gun systems. On 
the contrary, the success of fighter-bomber air- 
planes has made the development of adequate 
fire-control equipment for such airplanes ex- 
tremely important, and in particular, equip- 
ment that can be used with several weapons 
such as guns, rockets, and bombs. 

The objective of this report is to acquaint 
the reader with the important aerial gunnery 
equipment used or under development during 
World War II and the various problems en- 
countered in the development and evaluation 
of this equipment. The best way to have met 
this objective would have been to make this 
report a self-contained text book on aerial 
gunnery. This was impossible for many rea- 
sons, the principal one being lack of time. The 
method chosen was to give a descriptive ac- 
count of the problems encountered and the 
work done and to provide the reader with a 
carefully selected bibliography. This bibliog- 
raphy contains only a small fraction of the 
technical reports available on the subject but 
will be sufficient to provide the interested de- 
velopment engineer with the background on 
which to build future work. There are two other 
volumes of the Summary Technical Reports of 
NDRC containing material on aerial gunnery. 
The first is that on Military Airborne Radar 
Systems^ prepared by the Radiation Laboratory 
of Massachusetts Institute of Technology, and 
the other is on Analytical Studies in Aerial 
Warfare prepared by the Applied Mathematics 
Panel of NDRC.^ In addition there is an ex- 
cellent summary of the work in aerial gunnery 
which was done by the Applied Mathematics 
Group of Columbia University^ and a bibliog- 
raphy of reports prepared by that group.** All 


of this material should be given careful con- 
sideration in any future fire-control work. 

The contributions of Section 7.2 of NDRC 
to the field of aerial gunnery consist mainly of 
the coordination of the work of the Navy, the 
Army Air Force and the various civilian or- 
ganizations concerned, and the development 
of methods and equipment for assessing aerial 
gunnery systems. In both cases the initiative 
for the work came largely from the section. 
There was such a variety of gunnery equipment 
under development in the Services and in in- 
dustry that the section undertook very little 
of this work. The one major equipment lack 
was in the field of assessment, and the section 
put its major equipment development effort into 
correcting this situation. The coordination work 
in aerial gunnery done by the section was a 
substantial part of its effort in aerial gunnery 
and was brought about principally because 
there was no effective planning and coordinat- 
ing agency in the Army Air Force for this 
purpose. The two full time members of the 
section primarily concerned with aerial gunnery 
were the writer, who was a member of the 
section from September 1941 until he resigned 
to join the office of the Secretary of War in 
May 1945 and Dr. H. C. Wolfe, who was with 
the section from June 1944 until its termination 
early in 1946. The work in aerial gunnery was 
started by the section's chairman. Dr. S. H. 
Caldwell, when the Fire Control Section of 
NDRC (now Division 7) was first organized in 
1940. He continued his able leadership in this 
work in spite of the increasing pressure of 
other section responsibilities. It should also be 
noted that even though the writer and Dr. 
Wolfe were the only full-time members of the 
section devoting their time to aerial gunnery, 
all the other members of the section contributed 
to the work in varying degree and the work 
would have been much less successful without 
their assistance. 

The development work of the section in aerial 
gunnery was carried on almost entirely by six 
contractors. Reference is made to their work 
throughout the body of this report. The fol- 


178 


PREFATORY COMMENTS 


lowing is a list of these contracts with the cor- 
responding service directive numbers and an 
indication of the type of work. 

1. OSRD Contract OEMsr-330; Directive 

NO-268. 

Contractor : The Franklin Institute, Phil- 
adelphia, Pa. 

Work: Tracking Studies, Own Speed Gun- 
sight. 

2. OSRD Contract OEMsr-732; Directives 

AC-47, AC-128, NA114. 

Contractor : University of Texas, Austin, 
Texas. 

Work: Development and construction of 
testing machine for flexible gun- 
nery systems and tests on such 
systems. 

3. OSRD Contract OEMsr-991 ; Directive 

NO-152. 

Contractor: Jam Handy Organization, 
Detroit, Michigan. 

Work : Development of own speed type of 
assessor and gunsight. 

4. OSRD Contract OEMsr-992 ; no direc- 

tives. 

Contractor: General Electric Company, 
Schenectady, N. Y. 

Work: Development of improved Central 
Station Computer. 

5. OSRD Contract OEMsr-1237; Directives 

AC-36, NO-265. 

Contractor : Columbia University, New 
York, N. Y. 

Work : Development and use of electronic 
equipment for simulating Airborne 
Fire Control Systems. 

6. OSRD Contract OEMsr-1276; Directives 

AC-119, NA-161. 

Contractor : Northwestern University, 
Evanston, Illinois. 

Work: Development of equipment and 
methods for the assessment of 
aerial gunnery equipment and the 


installation and operation of such 
equipment for the Navy. 

In addition to these contractors. Section 7.2 
supervised the work of several other contrac- 
tors doing work for NDRC under the general 
direction of other divisions. The most important 
of these are the General Electric Company, the 
Sperry Gyroscope Company, and the Fairchild 
Camera and Instrument Company, all of whom 
were developing computers or other equipment 
for airborne central station fire-control systems. 

The section acted as a consulting group to 
the Navy and the Army Air Force on airborne 
fire-control matters and advised many members 
of both Services on special problems. One of 
the best examples of this work is the participa- 
tion of the section in the Joint Army-Navy- 
NDRC airborne fire-control committee. This 
committee was organized early in 1944 pri- 
marily to organize and direct the aerial gunnery 
assessment program of the Army Air Force 
and to coordinate this program with a similar 
one being undertaken by the Navy with the as- 
sistance of Section 7.2. Under directive AN-5 
the section was asked to provide the leadership 
of the committee. The section asked the writer 
to undertake this work and he was the com- 
mittee's chairman from its organization until 
its work terminated at the end of the war. The 
chairman was very ably assisted in this work 
by Dr. Saunders MacLane of the Applied 
Mathematics Group of Columbia University 
who was vice-chairman. After the gunnery as- 
sessment program was well under way, the 
committee became largely a technical forum on 
airborne fire control which met once each 
month. It was well attended by key people from 
both the Army and the Navy. While the com- 
mittee held no authority, it received excellent 
cooperation from its members and succeeded in 
contributing substantially to the coordination 
and direction of the fire-control development 
work of both the Army Air Force and the Navy. 

John B. Russell 


ONFIDENTTAL 


Chapter 14 


GENERAL SURVEY OF AERIAL GUNNERY 


» ^ • SITUATION AT THE START OF 
WORLD WAR II 

W HEN THIS COUNTRY entered the war in De- 
cember 1941, there was available practi- 
cally no gunnery equipment suitable for fight- 
ing the aerial battles. Fighter planes had the 
new .50-caliber machine gun but no suitable 
gunsight to use with it. The only fighter gun- 
sight available at that time was the old ring- 
and-bead sight. This ring-and-bead sight was 
subject to parallax errors due to the motion of 
the pilot’s head. However, what was more seri- 
ous was the fact that this sight was only a 
means for laying off an estimated amount of 
lead and was of no aid to the pilot in comput- 
ing the correct amount of lead. The parallax 
error was eliminated before long by the intro- 
duction of a refiector-type sight. This sight 
produced, by optical means, an illuminated 
reticle which appeared to be at infinity. This 
gave the pilot a reticle whose direction and size 
were independent of the position of his head. 

It was not until nearly the end of the war 
that a computing sight was available for the 
fighter airplane. This was the single-gyro type 
of sight developed by the British and known by 
them as the MK Il-d. This sight had originally 
been developed for use with flexible guns for 
bombing defense, but the greater importance of 
fighter gunnery caused them to adapt it to the 
fixed-gun fighter airplane. The Army Air Force 
was not particularly enthusiastic about this 
sight because it was felt that certain inherent 
errors were too large. The British, however, 
defended the use of this sight on the basis that 
in spite of these errors it gave the fighter pilot 
a means of increasing the accuracy of his shoot- 
ing several times. The Army Air Force was 
finally convinced of this fact through the efforts 
of the Navy and Section 7.2 of NDRC, and 
eventually adopted an American version of it 
in their own fighter plane. This Army Air Force 
version was known as the K-14 sight. 

During the early phases of World War II 
very little development was done in this country 


on a fighter’s gunsight. As with the British, 
most development work on gunsights was done 
on sights which were intended for use in flex- 
ible gunnery. In the last phase of the war, 
development work was started on a sight in- 
tended for fighter gunnery. This has resulted 
in the development of the A-1 gunsight which 
can be used not only for gunnery but for rock- 
etry and bombing as well. In fact, the develop- 
ments in the use of fighter-bombers during the 
war have shown the necessity of using a com- 
puting sight in the fighter which can be used 
for all the attack functions of the fighters. 

The early B-17’s had practically no defensive 
armament. There were no gun turrets, all guns 
being in a flexible mounting and hand held. 
There were no guns in the tail. The only sight 
used was a ring-and-bead sight which was sub- 
ject to bad parallax error. This error was much 
more severe in the use of flexible guns than it 
was in the use of fixed guns in a fighter. In 
addition, the problem of estimating the lead 
required to hit an attacking fighter was a very 
difficult one. At the beginning of the war this 
country had no adequate rules for estimating 
this lead, no suitably trained gunners or any 
adequate means of training them. Experience 
gained by the British in the European Theater 
showed the necessity for a much greater de- 
fense of heavy bombers than was available on 
the B-17 or the B-24. As a result, twin gun 
turrets were developed for use on both these 
airplanes and guns were installed in the tails. 
Even with these additional guns and improved 
mounts, only a fixed sight was used. These were 
optical reflecting sights which eliminated the 
parallax error by providing an illuminated 
reticle projected to infinity. The control of the 
guns was considerably improved in the case of 
the turret mount by the use of a power control. 
In fact the added weight and size of the turret 
mount over that of the simple hand-held mount 
made it impossible for the gunner to exercise 
control without the assistance of some sort of 
power drive. 


179 


c 


CONFIDENTIAL 


7 


180 


GENERAL SURVEY OF AERIAL GUNNERY 


The first methods which were taught and 
used for estimating lead were of the so-called 
apparent-speed type. The gunner was expected 
to determine the relative motion of his target 
during some estimated interval of time and 
then set a lead computed from this observation 
by the use of a rule. Gunnery schools taught 
this method and gave the gunners practice in 
it largely on ground ranges. Very little time 
was devoted to practice in the air. A great deal 
of the practice on the ground was in the form 
of skeet shooting. This certainly gave the 
gunner a fair amount of experience in handling 
and firing his gun and in estimating lead re- 
quired by a moving object fired at from a sta- 
tionary platform. However, the effect of this 
practice was to make him lead the target in the 
direction in which the target appeared to be 
moving through the air. When this was trans- 
ferred to the situation of an actual aerial com- 
bat, it often caused him to lead an attacking 
enemy fighter in the direction in which the 
fighter was moving in the air. This lead was in 
exactly the wrong direction because even 
though the fighter may have been headed in 
the same general direction as the bomber being 
defended, the actual relative motion of the 
fighter was usually toward the tail of the 
bomber. The lead should always have been in 
the same direction as the relative motion of the 
target. This fundamental error was the cause 
of many of the misses experienced during the 
early days of the war. 

2 POSITION FIRING RULE 

The British were the first to introduce a 
sound method of estimating the lead required 
to hit the attacking enemy fighter. It was known 
that a fighter would almost always attack a 
bomber in such a way that the fighter’s guns 
would bear on the bomber during as large a 
portion of the attack as possible. This caused 
the fighter to fly a curved course approximat- 
ing that known as a pursuit course. For such a 
course, if the fighter’s true airspeed and the 
bomber’s true airspeed were known reasonably 
accurately, the required lead for hitting the 
fighter was known and would be the same for 
every such attack. Furthermore, the magnitude 
of that lead would depend, approximately. 


only on the bearing angle of the fighter 
relative to the bomber’s line of flight. The direc- 
tion of this lead would be in the plane of action 
of the fighter, which was determined by the 
position of the fighter and the line of flight of 
the bomber. This led to the British zone firing 
method of estimating leads for bomber defense. 
The U. S. Navy and the Army Air Force fol- 
lowed the British lead and developed a similar 
method known as position firing. This method 
was eventually used for the defense of all U. S. 
Army bombers until some sort of a sighting 
mechanism could be provided. Subsequent tests 
and analyses showed that the position firing 
rule, while not particularly accurate, was more 
accurate than any of the methods previously 
used. It was not until almost the end of the war 
that anything like an adequate gunsight was 
available for all the various gun positions of 
the B-17 and B-24. 

One improvement in the use of the position 
firing rule, which came just before the end of 
the war, was the introduction of the K-13 sight. 
This sight was eventually to be put into all gun 
positions not equipped with a computing sight. 
The K-13 sight was simply a mechanism for 
computing the lead required by the position 
firing rule, and indicating it to the gunner auto- 
matically. The biggest error in the use of the 
position firing rule was due to the inability of 
the gunnery to accurately estimate the angle 
off, or bearing angle, of the enemy fighter and 
to lay off the corresponding lead. The K-13 
sight did this for the gunner and gave him an 
opportunity to do a better job of tracking and 
of estimating range. The K-13 sight was subject 
to all the errors inherent in the position firing 
method. 

143 LEAD-COMPUTING SIGHTS 

The only computing sight for flexible gunnery 
which saw any use during the war was one of 
the various forms of the Sperry lead-comput- 
ing sight. The early models of this were the 
K-3 and K-4 sights which were used in the up- 
per and lower turrets of the B-17, respectively. 
This sight computed a lead in terms of the 
range to the target and its relative angular 
velocity with respect to the bomber. It gave a 
lead which was satisfactory for a variety of 


TURRET CONTROLS 


181 


types of attack. One of the fundamental dis- 
advantages of the position firing method was 
that the leads determined by this method were 
correct only for one type of relative course on 
the part of the attacking fighter. As soon as 
the fighter deviated from this course the leads 
given by the position firing method were in 
error by a very large amount. The K-3 and K-4 
sights, however, were able to give leads which 
depend primarily on the relative motion of the 
target and, therefore, were usable in a wider 
variety of situations. They also provided leads 
whose accuracy depends on the actual course 
flown by the target but to a much less extent 
than for the K-13 sight. 

Considerable work was done during the war 
on the development of an improved lead-com- 
puting sight. The British led the way with the 
first major improvement by introducing the 
single-gyro type of sight which they call the 
MK ll-c and which was later modified for use 
as a fighter sight. In this country, most of the 
development effort put on sighting systems for 
flexible guns was devoted to elaborate remote- 
control systems. The benefit to be gained by a 
suitable lead-computing sight for use on planes 
such as the B-17 or B-24 was not fully appre- 
ciated. When the British MK II-c was first 
demonstrated to the Army Air Force it met 
with surprising lack of interest. It was largely 
through the efforts of Section 7.2 of NDRC that 
the Army Air Force finally gave the MK II-c 
serious consideration. This sight provided the 
same type of lead computation as the Sperry 
lead-computing sights, with one important 
added advantage ; namely that it computed the 
lead in terms of the actual angular rate of the 
target relative to the bomber and, therefore, 
was not affected by any angular motion of the 
bomber. It did not have all the accuracy that 
the Army Air Force desired but would provide 
a much more accurate means of shooting than 
had previously been available. The principal 
source of inaccuracy of both the Sperry and the 
single-gyro lead-computing sights was the in- 
ability of the gunner to range on the target and 
track in direction simultaneously with sufficient 
accuracy. 

Another improved lead-computing sight was 
one developed by Fairchild and was known as 
the K-8 gunsight. This sight was in production 


at the end of the war, and a few had been in- 
stalled and put into use before hostilities ended 
in the European Theater. The major difference 
between this sight and the others was that it 
made use of electrical circuits for computing 
time of flight and the ballistic corrections. It 
did not use a gyro and therefore was subject to 
the same type of errors as the Sperry K-3 and 
K-4. However, work was being done on the 
development of a gyro for use with this sight. 

1^-* TURRET CONTROLS 

The early turrets, while power driven, had 
only very simple hand controls for controlling 
the pointing of the gun. The simplest gun 
mount, which was the hand-held mount, was 
position controlled. This means that the gunner 
grasped the rear of the gun and by his own ef- 
fort pointed it in the desired direction. The 
force necessary to move the gun and hold it 
against the force of the wind stream had to be 
provided by the gunner. This made it very dif- 
ficult to point the gun accurately. The use of 
power control made it unnecessary for the 
gunner to exert any great amount of force in 
controlling the position of the gun. It also made 
it possible to use a larger and heavier mount 
which would provide the gunner with a seat 
which carried him around with the gun. The 
usual type of control for such turrets was a rate 
control in which the angular rate of motion of 
the gun was more or less proportional to the dis- 
placement of the control handle. Each manu- 
facturer had his own choice for the rate-control 
constant. As a result, some turrets were much 
easier to control than others. Also, this made it 
difficult to do satisfactory tracking with some 
turrets. 

At first very little was known about what the 
turret control design should be in order to 
provide optimum tracking. It was felt by many 
that a slightly more complicated turret control, 
known as aided tracking, would provide the 
gunner with a greatly improved means of doing 
accurate tracking. Section 7.2 undertook to 
study this situation by means of a tracking 
study carried out at The Franklin Institute. 
This study indicated that the use of aided track- 
ing would greatly improve the accuracy of 
tracking with power-driven turrets. However, 


182 


GENERAL SURVEY OF AERIAL GUNNERY 


it was impossible to make use of this knowledge 
before the end of the war. New turret controls 
which were under development during the latter 
part of the war were to include the aided track- 
ing feature. 

An additional refinement which was to be in- 
stalled in these new turrets, with very little in- 
crease in space or weight, was the stabilization 
feature. Even with power control of turrets it 
was necessary for the gunner to operate the 
controls in such a way that the motion of the 
gun not only followed the relative motion of 
the target with respect to the bomber, but also 
compensated for any angular motion of the 
bomber itself. This meant that in rough 
weather or during evasive action it was dif- 
ficult for the gunner to do satisfactory tracking. 
As a matter of fact, the accuracy of tracking 
obtained under these conditions was so bad 
that shooting was almost entirely ineffective. 
By stabilizing a turret, it is possible to auto- 
matically eliminate the effects of a bomber mo- 
tion. This leaves the gunner with only the prob- 
lem of tracking the relative motion of the 
target. Tests of experimental turrets under 
simulated conditions show that the marked 
improvement in tracking accuracy expected is 
actually attained. 

CENTRAL STATION SYSTEMS 

The development of the B-29 brought up a 
new and difficult problem in bomber defense. 
The large size of the airplane called for a large 
number of gun positions and more elaborate 
arrangements for coordination between these 
positions. The problem of lead computation was 
made much more difficult because of the higher 
speed of this bomber. The use of locally con- 
trolled turrets appeared impractical because of 
the decision to design the B-29 so that it could 
be used at high altitude under pressurized con- 
ditions. It was primarily for this reason that a 
remote-control type of system was chosen for 
the defense of the B-29. This called for sighting 
stations within the pressurized sections of the 
plane and a number of remotely controlled gun 
turrets which were in the unpressurized sec- 
tions of the airplane. An elaborate computer 
was necessary to compute the required kine- 
matic lead, the ballistic correction, and the cor- 


rection for parallax due to the large distance 
between the sighting station and the turret 
under control. 

Two major developments were carried out to 
provide an adequate fire-control system for the 
B-29. One of these was carried out by the 
Sperry Gyroscope Company and the other by 
the General Electric Company. Before either 
of these developments was completed, the Army 
Air Force decided to go into production on the 
GE system. As a result, the Sperry develop- 
ment was never entirely completed. Work was 
carried out to the point where a developmental 
model was completed and in operation. This 
model was never tested by the Army Air Force. 
However, it appeared to have several features 
which were superior to the GE system put into 
production, and which should be reconsidered 
in any future development work. 

The GE system was finally produced in ade- 
quate quantities and saw service in the air war 
over Japan. While it appears to have done an 
adequate job under the conditions which existed, 
it was far from a satisfactory system. The sight- 
ing station was difficult to control and this re- 
sulted in rather poor ranging and tracking accu- 
racy. The lead computation suffered from serious 
time delays and was limited in many ways by 
the particular design chosen. The computer 
was large, heavy and complicated and intro- 
duced a rather serious maintenance problem. 
While there are many features of this system 
which should be retained, it is probable that 
at the present time a more useable and more ac- 
curate system could be built which is consider- 
ably lighter, much smaller in size, less ex- 
pensive and far easier to maintain. A very 
large amount of time was spent on getting the 
bugs out of the initial GE production and in 
adjusting the system to give satisfactory ac- 
curacy. Considerable development work was 
done near the end of World War II to improve 
the GE system by simplifying the computer 
and by providing a more adequate sighting 
station. 

TRAINING 

All through the development work during 
the war, very little attention was paid to the 
human factor. In all the gunnery systems which 


CONFIDE^Tn(:| 

— . y/ 


ASSESSMENT 


183 


saw any use during the war, the ability and 
skill of the gunner was the predominant factor 
in determining the overall accuracy of the 
system. Little information was available to the 
designer on the effect of the control system de- 
sign on the ability of the gunner to use the 
equipment. Many designs, such as that of the 
sighting station on the B-29 system were 
adopted and put into production before any 
information was available on the ability of the 
gunner to use the equipment or the difficulty in 
training him in its use. It is now recognized 
that closer cooperation between the training 
people, psychologists, and the equipment de- 
signers would have resulted in the production 
of equipment which could be used with much 
greater accuracy. Another difficulty which arose 
was due to the fact that the Units in the Army 
Air Force responsible for training gunners 
seldom saw the equipment which the gunner 
was supposed to use until after it had actually 
reached an operational theater. This meant that 
the theaters were often receiving gunners who 
had had no adequate training with the equip- 
ment they were to operate. It also meant that 
equipment was often sent to the theaters in 
which the time required for adequate training 
was much too great. An additional difficulty due 
to this lack of cooperation with the training 
people was the fact that they were unable to 
develop and build training equipment in time to 
start training in the use of this new equipment. 
Many of these problems were on the way to 
being solved toward the end of the war, and it 
is hoped that this experience will not be for- 
gotten in the future. 

ASSESSMENT 

Probably the most important reason for the 
lack of adequate direction of the development 
program in aerial gunnery was due to the non- 
existence of any adequate method for assessing 
the performance of such equipment. The first 
program for providing such assessment facili- 
ties was started by Section 7.2. This section 
undertook to develop an elaborate testing 
machine at the University of Texas. This ma- 
chine would handle a complete local turret 
system, including the gunner. An artificial 


target was provided which could be made to 
fly any chosen attack course. Simple motion 
of the gun platform or bomber could be simu- 
lated. A means was provided for measuring the 
accuracy of the final gun position at every point 
during the attack. Conditions were reproduc- 
ible so that any attack could be duplicated for 
various systems and with various gunners. This 
machine provided an accurate way of determin- 
ing the overall performance accuracy of the 
flexible gunnery systems. While it did not simu- 
late many of the psychological conditions which 
existed in the air under combat, it did provide 
a quick and accurate means of assessing certain 
systems. After the original machine was com- 
pleted, two additional machines were built, one 
which was installed at Wright Field and the 
other at the Naval Air Station, Patuxent River. 
These machines made it possible to do most of 
the assessment work which is necessary for 
studying and evaluating experimental and final 
models of flexible gunnery systems. It is safe 
to say that if these machines had been available 
at the beginning of the war, the present state of 
flexible gunnery would have been far superior 
to what it is at present and many man-hours of 
effort and considerable money would have been 
saved. 

A second method of assessment, which was 
finally developed, was one which could be used 
in flight testing flexible gunnery equipment. 
This system was developed under the general 
direction of the airborne fire control committee 
and is now in use at both the Army Air Force 
Proving Ground, Eglin Field and the Naval 
Air Station, Patuxent River. The equipment 
under test is flown and operated under simu- 
lated combat conditions with an actual fighter 
airplane making simulated attacks on the 
bomber. It provides operating conditions which 
are much more realistic than any which could 
be provided on the Texas tester. Most of the 
data was recorded photographically and later 
analyzed. Several methods were developed for 
the analysis of this photographic data, one de- 
pending largely on the use of charts, and the 
other on the use of special machines developed 
by the Northwestern Technological Institute. 

A third method of assessment, which reached 
a high state of development during the war, was 
that of mathematical analysis. The Applied 


/CONFIDENTIAL 


184 


GENERAL SURVEY OF AERIAL GUNNERY 


Mathematics Groups at Northwestern and 
Columbia Universities carried out mathematical 
analysis of a number of production and develop- 
mental gunnery systems. Such analyses are 
extremely valuable in predicting errors while 
a system is in a design stage, and in determin- 
ing the various sources of these errors. These 
analyses led to improved designs and calibra- 
tions of such equipment. All three methods of 
assessment should be used in any future devel- 
opment of aerial gunnery equipment. 

14.8 RADAR 

Radar played a very important part in the 
winning of this war. However, its effect on the 
success of aerial gunnery was almost nil. Very 
early in the war a large amount of effort was 
put into developing a completely automatic 
tracking and ranging radar for use in the de- 
fense of heavy bombers. A system was de- 
veloped which was satisfactory from a per- 
formance standpoint. However, it was com- 
plicated, costly, and large and was therefore 
never used. Later, simpler systems were de- 
veloped which could be used for determining 
range only and later others were developed for 
manual tracking in position also. The develop- 
ment of a complicated, costly, automatic sys- 
tem at the beginning of the war considerably 
delayed the development of simpler systems 
which might have been put into use during the 
war. At the close of the war, the simpler sys- 
tems had been put into production. The whole 
gunnery radar development program suffered 
very seriously from the lack of adequate direc- 


tion from the Army Air Force and the lack of 
good coordination between the fire-control and 
the radar groups. 

9 PLANNING AND CONTROL 

Now that the war is over, future development 
work on aerial gunnery systems should be done 
with far more coordination and direction than 
existed during the war. Most of the leadership 
and initiative in such development work during 
the war came from industry. There was no 
adequate group within the Air Force which 
could direct the development of such equipment 
and provide an integrated program. The Arma- 
ment Laboratory at Wright Field, which was 
charged with this responsibility, had neither 
the number nor the quality of personnel re- 
quired to provide the necessary direction. 
Furthermore, in the early part of the war one 
or two individuals in authoritative positions 
were unable to see the advantages which might 
be gained by receiving the cooperation of tech- 
nically competent civilians. This made it difficult 
to get the most from the available development 
facilities and considerably delayed the work of 
developing new gunnery systems. In fact, it is 
probable that more competent direction from 
the Army Air Force during the development of 
the GE system would have resulted not only in 
a better system but in a considerable saving in 
time and money. The success of any future 
development of this sort depends on the ability 
of the Army Air Force to build up and maintain 
a competent development group which can plan 
and direct such a development program. 




^O^IDEimAL' 9'l 


Chapter 15 


GENERAL PRINCIPLES 


TARGET COURSES 

T he accuracy of all fire-control devices de- 
pends in a varying degree on the course 
traversed by the target. In the field of aerial 
gunnery this is particularly true. Fortunately, 
the general type of course that an attacking 
fighter may fly and at the same time do ef- 
fective shooting at a bomber is rather limited.*' 
This philosophy has led to the development of a 
simple gunsight known as a vector or own-speed 
sight which is designed to operate against the 
most common type of attack, which is a pursuit 
course attack. The more complicated lead-com- 
puting sights and remote-control systems are, 
the less dependent are they upon the actual 
course flown by the target, but they are still 
sensitive to it to a certain extent. As new 
weapons are developed and put into use against 
attacking fighters, the actual attack course used 
by the fighter will change. This will make it 
necessary to alter the design of gunsights used 
for the defense of bombers, either to adapt them 
to these new courses or make them less sensitive 
to the type of target course. 

In order to understand the way in which a 
gunsight is affected by the particular course 
flown by the target, it is necessary to under- 
stand something about the various attacks that 
can be flown by an airplane and how these affect 
the relative course of the target as viewed from 
the bomber being defended. During World War 
II, with few exceptions, fighter airplanes car- 
ried fixed guns. These guns were pointed ap- 
proximately along the line of flight of the 
fighter airplane. They were elevated above this 
line of flight by a small amount to allow for the 
effects of gravity. During an attack the fighter 
was flown in such a way that during the most 
important portion of this attack, which was 
when the fighter was in effective range of the 
bomber, the fighter^s guns were continually 
bearing on the bomber. The bomber under at- 

*This may not continue to be true in the future if 
turreted fighters come into use. 


tack was normally flying a straight and level 
course. This was particularly true if the attack 
was being made while the bomber was in forma- 
tion or on its bomb run. On such a course the 
bomber presented the fighter with a much easier 
target than if the bomber were taking evasive 
action. If the bomber for any reason had 
dropped out of the usual formation and was by 
itself, it would generally take evasive action 
when under attack from an enemy fighter. This 
made it much more difficult for the attacking 
fighter to get hits and was often sufficient to 
allow the bomber to escape. The determination 
of the course of the bomber and of the attack- 
ing fighter during actual combat conditions was 
very difficult. In fact there were no accurate 
means for observing the relative motion of the 
two planes during combat. Observations of an 
attacking fighter by gunners on the bomber 
under attack proved to be completely inadequate 
to give more than a very rough idea of the 
course of the attacking fighter. 

Since it was necessary to know something 
about the course of an attacking fighter to 
properly design a gunsight for use on the 
bomber and to get some idea of its accuracy, it 
was necessary to study the operation of such 
sights assuming idealized or simplified fighter 
attack courses. The simplest course which could 
be conceived was that for which the attacking 
fighter was flying a straight-line course relative 
to a bomber which, itself, was flying a straight 
and level course. The first analyses that were 
made of the performance of lead-computing 
sights were for this type of straight-line course. 
It was obviously very unrealistic but served to 
provide some understanding of the performance 
of the sight. The simplest type of target course 
which is reasonably realistic is the pure pursuit 
course. For this course it is assumed that a 
bomber flying a straight-line course at constant 
speed is under attack by a fighter flying at 
constant speed in such a way that at all times 
the fighter’s line of flight is pointed directly 
at the bomber. These assumptions do not allow 




lONFIDENTIAL 


185 


186 


GENERAL PRINCIPLES 


for the variable speed which always occurs dur- 
ing a fighter attack nor for the lead which the 
fighter must take in order to get a hit on the 
bomber. However, the pure pursuit course ap- 
proximates an actual fighter attack course 
sufficiently well that a fair understanding of 
the operation of a flexible gunsight can be ob- 
tained by studying its use against such a course. 
Very early in the war an analysis of the pure 
pursuit course was made.® General equations 
were derived, completely specifying the relative 
positions of the bomber and the fighter for this 
situation. Tables were prepared giving all the 
numerical data of interest on a variety of such 
pure pursuit courses, including the lead re- 
quired by the relative motion of the attacking 
fighter for accurate shooting from the bomber. 

Because it was known that an attacking 
fighter never actually flew a pure pursuit 
course, there was always the question as to how 
good an approximation was being made by as- 
suming that the fighter would fly such a course. 
The lack of any reliable experimental data made 
it necessary to attempt to answer this question 
and get more reliable information on the 
courses actually flown by using analytical meth- 
ods. The two important factors which are not 
accounted for in the assumption that the fighter 
flies a pure pursuit course are the effect of the 
lead which had to be taken by the fighter, and 
the effect of the aerodynamic properties of the 
fighter airplane. It was known that the fighter’s 
line of flight did not coincide with the axis 
of its guns and, in fact, that the angle between 
them depended on such things as the airspeed 
of the fighter, the curvature of its actual flight 
path, the loading of the airplane, and skid. One 
of the early attempts to predict the course ac- 
tually flown by the fighter was for the case 
where its guns are continually pointing at a 
bomber in straight-line flight at constant speed. 
This course is known as an aerodynamic pursuit 
curve. If, in addition, the fighter flies in such a 
way that it always maintains the correct lead 
on the bomber under attack, it is said to be 
flying an aerodynamic lead pursuit curve. In 
each case it is assumed that the fighter is being 
flown perfectly, although the aerodynamic 
properties of the fighter airplane are being 
taken into account. One of the earliest attempts 
to derive the equations for the aerodynamic 


lead pursuit curve is described in reference 6. 
A complete set of equations'^ specifying the aero- 
dynamic pursuit curve has also been derived. 
The solution of these equations for a simple 
case, namely an overhead attack, was made*^ 
by the Applied Mathematics Group at Columbia 
University. They computed a number of actual 
courses for American fighters and finally made 
a fairly complete solution of the aerodynamic 
lead pursuit course problem.^ They eventually 
computed a number of aerodynamic lead pur- 
suit courses and gave the leads which must be 
taken by a gun on a bomber under attack in 
order to get hits on a fighter flying such a 
course.^^ These courses represent the most com- 
plete information on pursuit types of attacks 
which was available at the end of the war. 

While the Applied Mathematics Groups at 
Brown University and Columbia University 
were most active in the analysis of pursuit 
courses, several other organizations made 
studies of this problem. The Mount Wilson Ob- 
servatory prepared a set of charts of pure 
pursuit curves which were very useful.^^ The 
Douglas Aircraft Company made a very inter- 
esting study of pursuit-course attacks on high- 
speed bombers.^i They showed that with a 
high-speed bomber, the regions of attack might 
be sufficiently reduced that the bomber need only 
defend itself in the nose and tail cones. This 
was brought about by the fact that the types 
of pursuit attack which were possible were 
greatly limited by the effects of the high ac- 
celeration produced by the curvature of the 
attacking fighter’s course. The General Electric 
Company was interested in the types of attack 
that could be made against the B-29 and made 
an analysis of some of these attacks.^^ The Jam 
Handy Organization was interested in the 
analysis of attack courses for two principal 
reasons. They were manufacturing training 
films for the Navy and the Army and wished 
to make the attack shown as realistic as pos- 
sible. Also, they had under development a vector 
or own-speed type of gunsight. The results of 
some of their analyses are given in reference 
14. The Jam Handy Organization also carried 
out a flight experiment in cooperation with the 
Navy, to measure the actual courses flown by 
an attacking fighter. The course data obtained 
from this experiment are not too accurate but 



BALLISTIC LEAD AND TIME-OF-FLIGHT 


187 


did compare favorably with course data com- 
puted analytically.^^ 

During the latter part of the war both the 
Army Air Force Proving Ground Command at 
Eglin Field and the Naval Air Station, 
Patuxent River obtained a large amount of 
data on courses actually flown by attacking 
fighters. These data were obtained under ex- 
cellently controlled conditions and with rather 
elaborate test equipment. They are also the 
most accurate information on courses actually 
flown which was available at the end of the 
war. Some discussion of the method used will 
be described later. 

As has been mentioned, one reason for desir- 
ing to know the actual course flown by an 
attacking fighter is to determine the various 
factors of design in a flexible gunsight which 
is to be used to shoot down the fighter and to 
analyze the accuracy of this shooting. Another 
reason is to investigate the various regions of 
possible attack by a fighter and thereby deter- 
mine the regions in which a bomber is most 
likely to be under attack.^^ Reference 16 gives 
a good summary of the status of this problem 
at the end of the war. 

1-2 ballistic lead and TIME-OF- 
FLIGHT 

When shooting at a stationary target from 
a stationary gun, the gun is not pointed directly 
at the target but above it in order to com- 
pensate for the drop of the bullet due to gravity 
as it travels from the gun to the target. If the 
target is moving, the gun must be pointed ahead 
of the target in order to allow for the motion 
of the target during the period of time in which 
the bullet is traveling from the gun to the 
target. This period of time is usually referred 
to as the time-of-flight of the bullet. It depends 
upon the initial velocity of the bullet, the dis- 
tance to the target and to some extent the slow- 
ing down of the bullet due to air friction. The 
deviation between the actual direction of the 
fire and the line of sight to the target at the 
instant of fire, which is required by the motion 
of the target during the time-of-flight, is called 
the kinematic lead. The elevation of the gun 
required in the simple example cited, which is 
necessary to compensate for the fall of the 


bullet due to gravity, is called the ballistic lead. 

When firing from a gun which is on a rapidly 
moving platform, such as an airplane, an ad- 
ditional ballistic effect becomes very important. 
This is the effect of the relative wind caused by 
the rapid motion of the airplane. This relative 
wind causes the apparent trajectory of the 
bullet to be curved, and must be compensated 
for in order to obtain a hit on the target. This 
windage effect is a far more important ballistic 
lead or correction than that due to gravity. In 
order to compensate for this and to determine 
the correct amount of kinematic lead, the effect 
of this relative wind and the time-of-flight of 
the bullet must be known accurately under a 
wide variety of conditions. The extreme dif- 
ficulty of carrying out experiments in the air 
under conditions of flight makes it almost im- 
possible to measure these effects accurately. As 
a result, the best information available is ob- 
tained from analyses. The Ballistic Research 
Laboratory at Aberdeen has done a tremendous 
amount of work in analyzing the motion of a 
bullet fired from a moving airplane.^^' 2 o 

This work has led to the development of 
methods for computing the trajectories of a 
wide variety of bullets fired from a moving 
airplane. Such information has to be incorpor- 
ated in the design of any sight for use in a 
moving airplane. An improved method for 
computing these trajectories was developed at 
the General Electric Company.^i Tables of bal- 
listic lead and time-of-flight are available on 
all the common bullets from either the Ballistic 
Research Laboratory or the Armament Labora- 
tory at Wright Field. For the purposes of the 
design of gunsights or the analysis of their 
performance, it is desirable to express the in- 
formation contained in the ballistic tables by 
some form of an equation. This was done by 
the Applied Mathematics Group at Columbia^^ 
and also at the Laredo Army Air Field.^^ These 
formulas were found to be extremely useful 
and gave the time-of-flight and the ballistic lead 
with exceptional accuracy. 

Although all the numerical information per- 
taining to the trajectories of bullets fired from 
airplanes has been derived analytically, the 
Ballistic Research Laboratory finally was able 
to carry out an experiment in which certain 
trajectories were measured which could be 


Ji 


GONFIDENTIAL 


188 


GENERAL PRINCIPLES 


compared with the corresponding computed 
trajectories. This experiment served to check 
the analytical work and to further emphasize 
the difficulty of obtaining such information by 
experiment. In fact, the experiment consisted 
of firing from a moving airplane at a water 
target. While this was sufficient to check the 
analytical work experimentally, it was not a 
measurement of an actual trajectory under 
conditions that would normally be used in 
combat. 

3 true lead 

For any particular course being followed by 
an attacking fighter, it is possible to determine 
what true lead must be taken by the defending 
bomber in order to obtain a hit on the attacking 
fighter. The most obvious way to compute this 
lead, when the type of ammunition and the 
target course are known, is by the use of 
future time-of-flight. By future time-of-flight 
is meant the time of travel of the bullet from 
the instant of firing to the point where the 
target will be when it is struck by the bullet. 
If a particular point on the course of a target 
is taken as the future position or collision point 
for the target, it is possible to work backwards 
in time and determine from what point the 
bullet must have been fired in order to arrive 
at this future target position. In order for this 
process to be possible, the target course relative 
to the bomber must be given and the bomber 
must be flying in a straight-line course at a 
constant speed. Ballistic tables will give the 
time-of-flight of the bullet for the particular 
range between the bomber and the future posi- 
tion of the target, and will also give the neces- 
sary ballistic lead for the various conditions 
existing. The separation between the future 
position of the target and its position relative 
to the bomber at an instant of time earlier by 
this time-of-flight will be the desired kinematic 
lead. The accuracy of this method for determin- 
ing true lead is limited only by the accuracy of 
the information available on the ballistics of 
the bullet and the actual target course. It can 
be applied to cases where an assumed target 
course has been computed, such as pure pursuit 
courses, or where the target course has been 
determined experimentally. This method has 


been used extensively at the Army Air Force 
Proving Ground Command at Eglin Field and 
at the Naval Air Station at Patuxent River for 
determining the true leads corresponding to 
the various simulated fighter attacks made in 
the flight testing of flexible gunnery equipment. 

In analytical work where the equations of 
the target course are known in mathematical 
form, it is often possible to derive an equation 
for the true lead. One such formula for the 
case of a pursuit course is given in reference 
24. Much more complete and general formulas 
were worked out by the Applied Mathematics 
Group at Columbia University.^® This report 
gives the most complete analysis available on 
the general problem of determining true leads. 
The more difficult problem of determining true 
lead when the bomber is taking evasive action 
was studied by the Applied Mathematics Group 
at Columbia University,^® and by the Applied 
Mathematics Group of Northwestern Univer- 
sity.^®"^ Up until the end of the war, no attempts 
had been made to actually compute true leads 
in the case where the bomber was taking eva- 
sive action. A great deal of work had been done, 
however, in computing true leads for pursuit 
type of attack courses with the bomber flying 
in a straight line at constant speed. Tables giv- 
ing this information are available in references 
27, 28, and 10. They are also available in the 
results of tests at the Army Air Force Proving 
Ground Command at Eglin Field and the Naval 
Air Station at Patuxent River. 

15.4 principles OF LEAD COMPUTATION 

There are a number of basic principles which 
have been used in the mechanisms for com- 
puting lead in an actual gunsight. In general, 
ballistic lead and kinematic lead are computed 
separately in two different parts of the gun- 
sight and then combined to give the total lead. 
In all sights, some sort of an approximation is 
made to the true lead in order to simplify the 
mechanism since sufficient data are not known 
from which the true lead may be determined. 
In the simplest case, that of the fixed gunsight, 
the only information on the target course which 
is made use of is its bearing angle in the plane 
of action relative to the flight path of the 
bomber. The lead which the gunner is expected 




PRINCIPLES OF LEAD COMPUTATION 


189 


to use, and which is expressed by the position 
firing rules, is based on the assumption that the 
fighter is flying a pursuit course. It is also as- 
sumed that the only requirement necessary for 
obtaining a hit on the target is to give the bullet 
a velocity directed toward a fighter in the air 
mass at the instant of firing. Certain correc- 
tions are made for the curvature of the fighter’s 
path and the aerodynamic characteristics of the 
airplane, and these will be discussed in more 
detail in Section 16.2. 

In order to mechanize the position firing rule, 
and thereby produce an own-speed sight, it is 
necessary to build a mechanism which will pro- 
duce the vector sum of a vector representing 
the velocity of the bomber airplane and a vector 
representing the velocity of the bullet relative 
to that airplane. The sum of these two vector 
velocities is a third vector whose direction gives 
the initial direction of the bullet relative to the 
air mass. This has been accomplished in two 
ways. The first way is by means of linkages so 
arranged that they form a mechanical model of 
three vectors in question. The second way is to 
derive the equation for the required deflection 
and approximate the solution of these equations 
by means of a set of cams. In such a sight the 
output is a combination of both the kinematic 
and ballistic leads, although only to a first ap- 
proximation. In the more complicated gun- 
sights, which are of the lead by time-of -flight 
type, the kinematic and ballistic leads are com- 
puted separately. 

In general, the ballistic lead is computed by 
means of a set of cams whose position is deter- 
mined by the position of the gun relative to the 
bomber airplane and certain hand-set inputs 
allowing for the bomber’s speed, altitude, etc. 
Some of the cams are one dimensional, meaning 
that the output of the cam represents a function 
of a single input variable. Such a cam is a type 
most often seen in ordinary mechanisms. It 
may be a plate of irregular shape which, as it 
rotates, moves a follower on its edge. A varia- 
tion of this plate-type cam is where the fol- 
lower is moved radially along the side of the 
plate in a slot. A second variation is where the 
cam takes the form of a cylinder in which a 
follower is moved along the cam axially by 
means of a slot in the surface of the cylinder. 
This type of cam is usually described as a 


cylindrical cam, whereas the two previous types 
are referred to as plate cams. In all three cases 
the important variable is represented by the 
rotation of the plate or cylinder and the output 
is represented by the linear displacement of 
the follower. Where the output function de- 
pends upon two or more variables, several of 
these one-dimensional cams may be put in cas- 
cade, or one or more two-dimensional cams 
used. A two-dimensional cam is represented by 
an irregular surface which can be rotated and 
can also be moved axially. As these two motions 
take place a follower bearing on the surface is 
caused to move linearly, depending on the dis- 
tance of the surface from the axis of the cam to 
the point of contact. 

An electrical method analogous to these 
mechanical cam systems has also been used. 
This consists of electrical potentiometers in 
which the output voltage is determined by the 
position of a contact. The potentiometer wind- 
ing is so designed as to give the desired func- 
tional relation between output voltage and the 
input rotation. It is analogous to the one- 
dimensional mechanical cam. Cascade combina- 
tions of these potentiometers, where the output 
of one potentiometer supplies the input voltage 
for a second one, provides a means of multiply- 
ing functions of two variables. The main ad- 
vantage of the electrical type of cam or poten- 
tiometer over the mechanical cams is its small 
size, simplicity of construction and low cost. 
This means that an electrical computing device 
using these potentiometers can contain a great 
many more of these electrical cams than would 
be possible in an analogous computer using 
mechanical cams. 

A third method of computing a function of 
one or more variables is by the use of mechan- 
ical linkages. This method was not used in any 
flexible gunsights but was used to some extent 
in other computing systems. It shows con- 
siderable promise but as yet has not been ex- 
ploited to any great extent. 

In general, the ballistic computer part of a 
gunsight was designed to give an output which 
approximated to an acceptable degree of ac- 
curacy the ballistic data tabulated in the bal- 
listic table. In one case a ballistic computer 
was built involving a combination of linkages 
and gears which mechanized to the first order 


190 


GENERAL PRINCIPLES 


of approximation the equations giving the bal- 
listic deflections of the bullet. This was used in 
the GE computer for the B-29 and is discussed 
in more detail later. All of these various ballistic 
computers were used to compute the ballistic 
deflections due to windage and the time-of-flight 
of the bullet which was necessary for the com- 
putation of the kinematic lead. 

The usual method of computing kinematic 
lead was to determine the relative angular rate 
of the target by the best method possible, and 
multiply it by the approximate time-of-flight. 
The accuracy of this method was the subject of 
considerable analysis, and has been discussed 
in a number of reports which will be referred 
to in connection with the description of various 
types of lead-computing sights. The principal 
component for computing a kinematic lead by 
this method was some device for measuring the 
apparent angular rate of the target. The first 
form of mechanism for carrying out this an- 
gular measurement and for multiplying by time- 
of-flight was a mechanical variable-speed 
drive.2^ It was first used for this purpose in 
Sperry antiaircraft directors and the early 
Sperry airborne lead computing sight. The prin- 
cipal objection to the variable-speed drive as a 
means for computing kinematic lead is the fact 
that it is driven by the position of the gun rela- 
tive to the bomber airplane and, therefore, 
measures an angular rate relative to that air- 
plane. This means that any angular motion of 
the bomber airplane introduces an error into the 
determination of the relative angular motion of 
the target. An analogous electrical method has 
been used by Fairchild. In this case the angular 
velocity of the gun relative to the bomber is 
determined by means of an electrical tachom- 
eter whose field is excited by a voltage which is 
approximately proportional to the time-of-flight 
setting. 

In order to avoid the error in such systems 
(introduced by any angular motion of the 
bomber) , various gyroscopic methods of meas- 
uring angular rate have been used. The 
simplest of these is a rate gyro which is similar 
to the gyros used in aircraft rate-of-turn in- 
struments. This rate gyro is constrained so 
that it can rotate about only one axis which is 
perpendicular to its axis of spin. A spring is 
attached which tends to prevent rotation about 


this axis. If the spin axis of the gyro is made 
to rotate about a third axis which is perpen- 
dicular both to the spin axis and allowable rota- 
tion axis of the gyro, it will be displaced against 
the spring by an amount which is proportional 
to this forced rotation of the spin axis. Since 
such a constrained-rate gyro can give an indica- 
tion of rotation about only one axis, two such 
gyros are necessary in order to measure the two 
components of any two-dimensional rotation. 

A second method of using a gyro to determine 
angular rate is by means of a free gyro. This 
gyro is mounted in gimbals so that mechanically 
it is free to move in any direction. Torques 
are applied to it in one of several ways in order 
to cause it to process so that its spin axis will 
continually point at the object in space whose 
relative angular rate is to be determined. These 
processional torques may be applied by springs 
acting on the gimbal supporting the gyro, by 
an electric torque motor acting on these gim- 
bals, or by means of electric coils actually 
mounted on the gyro frame. One very ingenious 
method for using a free gyro was developed 
by the British and was used in the only gyro 
sight to see service during this war. In this 
case the gyro axis supported a copper dome 
which rotated with the spin rotation of the gyro 
and was subjected to a magnetic field produced 
by means of a magnet mounted on the housing 
supporting the gyro gimbal. The eddy current 
set up in the gyro dome due to its rotation pro- 
duced the desired precessional torques. 

A discussion of the principle involved in the 
use of both the rate gyro and the free gyro in 
a computing gunsight will be found in a re- 
port.^® The equations of operation of such a 
gyro gunsight for a simple case are discussed in 
references 31 and 32. More detailed analysis 
of the operation of gyro gunsights will be found 
in the discussion of the various types of sights, 
which appears in a later section. 

One problem which arises in the analysis and 
understanding of practically all gunsights is 
that of axis conversion.^^ For various practical 
reasons it is often necessary to compute the 
necessary lead in terms of two components. 
This is true not only for the computation of 
ballistic lead but also for the computation of 
kinematic lead. It is also necessary because in 
most cases the indication of computed lead is 


% 


JONFIDE 


PRINCIPLES OF LEAD COMPUTATION 


191 


given by the rotation of an optical line of sight 
about a pair of axes. In the early days of the 
war a number of mistakes were made in the 
analysis and development of gunsights because 
this problem was not fully appreciated. What is 
even more confusing is the fact that in many 
gunsights the axes with respect to which the 


two components of the ballistic lead are com- 
puted are different than the two axes with 
respect to which the two components of the 
kinematic lead are computed. This axis conver- 
sion problem is much more difficult in remote- 
control systems than it is for those in locally 
controlled turrets. 




CONFIDENTIAL 


Chapter 16 


LOCAL CONTROL SYSTEMS 


1 FIXED SIGHT SYSTEMS 

AT THE BEGINNING of World War II, the 
most common sight used in flexible gun- 
nery was the fixed sight. The earliest form of 
this was the iron ring-and-head sight. This was 
later replaced by an optical reflector type sight 
which produced an illuminated reticle projected 
to inflnity. This eliminated the parallax error 
which was so annoying with the ring-and-bead 
type of sight. The standard model of the Army 
reflector-type flxed sight was known as the N-8 
and a similar sight used by the Navy was 
known as the Mark 9. The major problem in 
developing these optical sights was to eliminate 
the difficulties due to airplane vibration and to 
provide a sufficiently large field of view. 

The early rules for laying off lead by means 
of these sights were the apparent speed rules. 
To apply these rules it was necessary to track 
the target long enough to get the reticle cen- 
tered on the target and then hold the gun and 
sight stationary for a predetermined length of 
time. This time was measured by saying some 
key word such as “elephant'^ which was sup- 
posed to take a length of time equal to the time 
of flight of the bullet at the opening range. The 
apparent relative motion of the target during 
this time interval was observed and then the 
gun and sight were moved so as to point ahead 
of the target by an amount equal to this ap- 
parent motion. 

There were two very serious difficulties with 
this system. The first is that it was impossible 
for a gunner to carry out these operations 
exactly. The second is that even if these rules 
were exactly followed, the leads computed by 
their application were seriously in error. This 
was realized by the Army Air Forces and the 
Navy in the early days of the war and con- 
siderable effort was made to determine what 
these errors were and to develop a more suitable 
set of rules. An elaborate analytical study of 
these rules and the proposed position firing rule 
was made by the Applied Mathematics Group 


at Columbia.^^ It was shown that even if the 
rules for the apparent-speed method were fol- 
lowed exactly, the resulting error in the leads 
would be as much as 25 to 50 mils in certain 
cases. The position firing rule which was finally 
adopted and used during most of the war on 
the B-17 and B-24 airplanes was found to be 
reasonably satisfactory. The errors run as high 
as 15 mils and have an average of perhaps 8 to 
10 mils. This may be considered as satisfactory 
in view of all the other difficulties which were 
encountered in pointing the gun and estimating 
the opening range. 

Since the only variable which the gunner 
takes into account in applying this rule is the 
position angle of the target, it will give satis- 
factory results only for the assumed set of con- 
ditions. This means that if the target attack 
course is materially different from that as- 
sumed in determining the rule, considerable 
error will be introduced into the lead. Also, the 
required lead will vary with the type of am- 
munition used, the altitude of the airplane and 
its indicated airspeed. All during the war this 
rule was under more or less continuous study 
and it was revised to meet changing conditions. 
Examples of this are the modification of the 
position firing rule for use as an emergency 
sighting system for the B-29^^ and the revised 
rule for use on the A-26.^® 

Even though the position firing rule is a 
relatively simple one, putting it into operation 
presented many difficulties. The gunner had 
to estimate the range to the attacking fighter 
in order to open fire at the appropriate max- 
imum range. Experience showed that in general 
this estimation of range was in error by a 
factor of about two and that he therefore 
opened fire at about twice the desired opening 
range. Another difficulty was the inability of 
the gunner to properly estimate the bearing 
angle of the target and the plane of action 
of the target. In the waist position the gunner 
was aided considerably in the estimation of 
the target bearing angle by the relative position 


1 CONFIDENTIAL | 

I V' 


192 


OWN-SPEED SIGHTS 


193 


of the gun with respect to the periphery of the 
waist hatch and the relative position of the 
wing and tail surfaces. In the tail position no 
part of the airplane was visible to aid in the 
estimation of the target bearing angle. For- 
tunately this was not too serious since the 
size of the required leads was relatively small. 

In a turret the estimation of the target 
bearing angle is also difficult. This difficulty 
of estimating a target bearing angle led many 
people to propose mechanisms for aiding the 
gunner in this estimation. In general these took 
the form of what is known as own-speed sights 
which mechanized the position firing rule and 
presented the gunner with information on the 
required lead. Toward the end of the war enemy 
fighters were making attacks which were some- 
what different than the pursuit type of attack 
and therefore the position firing rule being used 
was considerably in error. This also applies to 
the own-speed type of sights which will be 
discussed shortly. As a result, interest in ap- 
parent-speed rules was revived. A revised eval- 
uation of these methods was made and is con- 
tained in reference 37. 

16.2 OWN-SPEED SIGHTS 

During World War II a great number of 
own-speed sights were proposed. The idea goes 
back to World War I during which the so-called 
wind vane sight was proposed. The own-speed 
sights proposed during this war were of two 
general types. The first consisted of a linkage 
type mechanism generally containing gear 
drives which was a geometrical model of the 
various vector velocities which determined the 
required lead. The second type made use of 
cams for mechanizing the equations giving the 
required lead in terms of two components. 
Reference 38 contains a good summary of the 
various types of own-speed sights proposed. 
The first own-speed sights seriously considered 
were the K-10 and K-11 which were developed 
by Sperry. These were designed for tail and 
nose positions, respectively. They used three 
dimensional cams rather than linkages and 
were, therefore, somewhat limited in the range 
of coverage. This limitation prevented them 
from being used in any but the nose and tail 
positions. These particular sights were also 


excessively heavy and large and rather ex- 
pensive. A description of the K-10 and K-11 
sights and their underlying theory will be 
found in three Sperry reports.^^’^^*^^ 

Because of the simplicity of the own-speed 
type of sight and the lack of any lead-computing 
sight that was considered satisfactory, consid- 
erable effort was made to develop a suitable 
own-speed sight and get it into use as soon as 
possible. Section 7.2 started such a develop- 
ment at The Franklin Institute^^ in Philadel- 
phia quite early in the war. This development 
served to stimulate interest on the part of other 
development organizations as well as on the 
part of the Army Air Force. Developments 
using the own-speed principle were also car- 
ried on by the Jam Handy Organization. The 
original purpose of this development was to 
produce an own-speed type of assessor but it 
also led to the development of an own-speed 
sight. A description of the Jam Handy own- 
speed sight has been prepared by them.^^ The 
Jam Handy Organization (under a contract 
with the AAF) also developed a similar sight 
for the tail position of the B-25. A report on 
this development has been made.^^ One example 
of the wide variety of the sights proposed using 
the own-speed principle is given by the pro- 
posed modification of the standard B-17 tail 
sight.^^ 

Since the accuracy of the own-speed type of 
sight, as is the case with the position firing 
rules, depends so greatly on the actual course 
of the attack fighter, considerable effort was 
spent on ways of adapting the own-speed sight 
to meet these different conditions. If the attack- 
ing fighter made the assumed type of attack, it 
was only necessary for the flexible gunner to 
keep the reticle of his sight squarely on the 
target. The main indication that the fighter 
was flying a course different from the pursuit 
type of course assumed was the apparent atti- 
tude of the attacking fighter. The most impor- 
tant situation in which this condition arose was 
when an attempt was being made to provide 
support fire for protection of another bomber 
in the formation. In order to provide satis- 
factory support fire, using the own-speed sight, 
it was necessary for a gunner not only to apply 
rules which met this situation but to estimate 
the general aspect angles of attacking fighters. 


CONFIDENTIAL 


194 


LOCAL CONTROL SYSTEMS 


This situation was studied in some detail 
toward the end of the war, and the various 
proposed rules and their evaluation are dis- 
cussed in four reports — 46, 47, 48, and 49. 

With all the various proposals for an own- 
speed type of sight, it soon became necessary 
to make some sort of an evaluation of them 
and to decide on one or two best suited for the 
needs of the Air Force. The sight chosen was 
the Sperry K-13 which made use of a linkage 
type of mechanism. This sight was selected not 
necessarily because it was the most accurate 
sight available but because its accuracy was 
adequate and it could be put into use in the 
operational theaters most rapidly. The details 
of this sight are given in the Sperry instruction 
manual.^"^ An analysis of the errors of this 
sight under the conditions for which it was 
designed is contained in reference 51. 

Theory will show that the own-speed type 
of sight will accurately predict the required 
lead when the bomber is flying a straight course 
at constant speed, the attacking fighter is flying 
a pure pursuit course and the bullet has no slow 
down. In this case the input to the sight which 
accounts for the airspeed of the bomber is 
taken as the full value of the bomber’s airspeed. 
Due to the fact that the fighter is not flying a 
pure pursuit curve because of its aerodynamic 
properties and its own lead on the bomber, the 
use of the full value of the bomber’s airspeed 
will give erroneous results. This effect can be 
compensated for by using an appropriate per- 
centage of the bomber’s airspeed as the 
airspeed input to the sight. Various at- 
tempts‘^2,53,54 were made to evaluate this situa- 
tion and determine the optimum way to use the 
own-speed sight. 

In addition to the factor already mentioned, 
which might cause substantial error in the lead 
computation by the own-speed sight, there are 
several other factors of importance. One of 
these is the fact that the actual course of the 
attacking fighter does not lie in a plane of ac- 
tion having a constant elevation relative to the 
bomber. In particular, for high side attacks, 
the attacking fighter has an actual instantane- 
ous velocity which tends to carry it below the 
bomber’s line of flight. This has to be con- 
tinuously corrected by the fighter pilot and 
causes the instantaneous plane of action to 


continuously decrease in elevation. This results 
in an error in the lead produced by the own- 
speed sight which causes it to shoot too high. 
This error is partially compensated for by the 
gravity drop of the bullet which is not com- 
puted by the own-speed sight. Another impor- 
tant effect is that due to the attack angle of the 
bomber. It is assumed in using the own-speed 
sight that the actual vector velocity of the 
bomber is known. The direction of this velocity 
in space is normally not along the thrust axis 
of the bomber. In fact the angle between the 
actual velocity of the bomber and its thrust 
axis, which is known as the attack angle, is not 
constant. It varies with the airspeed and load- 
ing of the bomber. An average value of this 
attack angle is used in harmonizing the various 
own-speed sights with the guns. An attempt 
to take this factor into consideration was made 
in The Franklin Institute sight and in some of 
the Jam Handy developments. 


LEAD-COMPUTING SIGHTS 

The usual lead-computing sight is one in 
which the kinematic lead is computed by multi- 
plying an appropriate angular rate by a time of 
flight. It is so arranged that when a target is 
tracked with it, a measurement of angular rate 
is made continuously and this is multiplied by 
a time of flight setting which is derived from 
a measurement of range to the target. This 
measurement of range is ordinarily made stadi- 
ometrically. To do this the gunner operates 
the range control of sight so as to keep a reticle 
of varying size constantly bracketing the target. 
Toward the end of the war there were several 
projects whose objective was to introduce the 
use of radar determined range into the sight. 
This will be discussed in more detail in a later 
section. 

One basic difference between the lead-comput- 
ing sight and the own-speed sight is the manner 
in which the reticle moves with respect to the 
gun. In the own-speed sight the reticle is coupled 
to the gun in such a way that it always moves 
with the gun and gives the gunner very direct 
control over its motion. In this sight the con- 
trol of the reticle by the gunner is very direct 
and he would ordinarily not be cognizant of any 



LEAD-COMPUTING SIGHTS 


195 


motion of the reticle due to a change in lead. 
In the case of the lead-computing sight the 
reticle is floating. This means that a motion of 
the gun does not necessarily cause a direct cor- 
responding motion of the reticle. This is be- 
cause the lead indicated by the reticle of the 
lead-computing sight depends not only upon 
the gun position but also upon its rate of change 
of position. This causes the lead-computing 
sight to be somewhat more difficult to track with 
than the own-speed sight. This difficulty of track- 
ing is one important factor which must be taken 
into account in the sight design. 

The floating character of the reticle in the 
lead-computing sight also introduces a problem 
in regard to picking up and getting on the 
target. In general, during the preliminary 
slewing, the high angular rates produced will 
generate an excessive lead which must be re- 
moved before the gun is in correct position for 
firing. The transient response of the sight, 
which results in the removal of this excessive 
lead, may last for a time interval approximately 
equal to the time of flight setting of the sight. 
It also depends upon the design constants of 
the sight and is inseparably connected with 
the tracking characteristics of it. This tran- 
sient effect may also introduce an error into 
the lead when flring against a target having 
angular acceleration. This is because the 
transient effect is similar to a time lag and the 
lead which the sight computes is actually based 
on old data. An analysis of the lead-computing 
sight and its various effects is given in ref- 
erence 55, which also discusses the effects of 
computing the lead in terms of two components 
instead of directly in the plane of action of the 
target. 

The only lead-computing sights for flexible 
gunnery to see any extensive use in this war 
were the Sperry K-3 and K-4 sights. These 
sights were installed in the upper and lower 
turrets of the B-17. They use a mechanical 
type of rate-measuring device and multiplier. 
Rather severe approximations were made in 
designing the time of flight and the ballistic 
lead computer with the result that these sights 
are not too accurate. However, they gave con- 
siderably better performance than could be ob- 
tained with either position firing or the use of 
an own-speed sight. The sights were severely 


criticized by many people in the field and it was 
even suggested that they be removed and po- 
sition firing rules and a fixed sight be used in 
their place. Fortunately, this was not done and 
it was subsequently shown that the K-3 and K-4 
sights were far more accurate than a good 
many people realized. A description of these 
sights and an analysis of some of their errors 
appear in two Sperry reports.^®-^" Toward the 
end of the war an improved version of these 
sights was developed by Sperry and is known 
as the K-12.^® The K-12 sight provides a some- 
what better computation of time-of -flight and 
ballistic lead. The errors in the computed kine- 
matic lead that are inherent in any lead-comput- 
ing sight of this sort, can be minimized only by 
the proper choice of design constants and the 
proper calibration of the time-of -flight setting. 
The errors of the K-3 and K-12 sights have been 
the subject of rather detailed analysis.^® 

One of the fundamental sources of error in 
these sights is the fact that the angular rate 
of the target is measured with respect to the 
bomber. This means that an incorrect angular 
rate will be determined if the bomber has any 
angular motion of its own. This was the source 
of one of the most severe criticisms of the 
Sperry lead-computing sights. This would be 
particularly serious in a situation where it was 
necessary to use the sights while the bomber 
was taking evasive action. Fortunately this 
seldom occurred. The only important case was 
when an isolated bomber was being attacked 
and evasive action was being used as a means 
of protection. In the European Theater, this 
occurred when a single bomber had to drop out 
of formation for any number of reasons. In 
this case the bomber was generally under attack 
by several enemy fighters and it would have 
been difficult to defend it even with most ideal 
sighting systems. 

The first gyro type of lead-computing sight 
to see extensive use was not for plane-to-plane 
fire but was for antiaircraft fire. This con- 
tained two rate-measuring gyros which were 
used to compute the two components of kine- 
matic lead. The sight was used extensively with 
20-mm and 40-mm antiaircraft guns on ship- 
board. The sight was built by Sperry and was 
known as the Mark 14 gunsight. A rather de- 
tailed investigation of the theory and errors of 


196 


LOCAL CONTROL SYSTEMS 


this sight has been made.®® Even though this 
sight 'was designed and used for antiaircraft 
fire, its operation and its errors are similar to 
those that would be found in using such a 
sight for plane-to-plane fire. One error which 
is inherent in any lead-computing sight which 
determines lead in terms of two components is 
that due to the rotation of the sight about the 
line of sight. This particular error is described 
in reference 61. 

The most successful gyro type of lead-com- 
puting sight for aerial gunnery was the single- 
gyro sight developed by the British. This sight 
was originally developed for flexible gunnery 
for bomber protection. However, before it could 
be put into any extensive use for bomber de- 
fense, the need for its use as a fighter gunsight 
became very great. As a result the only use 
which this type of sight saw during the war 
was in fixed gun fighters. The Navy version of 
the gyro sight for flexible gunnery is known as 
the Mark 18 gunsight.®® The Army version is 
known as the K-15. A brief summary of the 
single-gyro type of sight as used in this country 
for both fixed and flexible gunnery is given in 
reference 62. 

When the single-gyro type of sight was first 
brought to this country by the British, the AAF 
showed very little interest in it. It was only 
through the efforts of Section 7.2 of NDRC 
that they finally gave it any serious thought 
and eventually adopted it for use in fixed gun 
fighters. On the other hand, the Navy was very 
interested in this sight from the beginning 
and was largely responsible for getting it into 
production, even though eventually the Army 
took over most of this production. A great deal 
of the work that was done by the Navy to re- 
design the sight for American use and get it 
into production was done by the Lucas-Harold 
Corporation.®^’®^ Their reports give an analysis 
of the sight and many of the design details. 

Because of the importance of the single-gyro 
type of sight, a great amount of effort was put 
into analyzing it and attempting to improve its 
design. Two detailed studies of the operation 
of the gyro and its supporting Hook’s joint 
were made.®®’®® A study of the general equa- 
tions of the sight will be found in references 
67 and 70, and a detailed analysis of the optical 
systems of the Mark 18 and K-15 in reference 


69. An analysis of the errors of the Mark 18 
sight when used against pure pursuit courses 
has also been made.^^’'^® 

The time-lag error which is inherent in any 
lead-computing sight can be minimized by a 
proper choice of the time-of-flight setting. If 
the time-of-flight setting which is used is the 
same as the actual time-of-flight to the present 
position of the target, the errors in the kine- 
matic lead will be smallest when the sight is 
used against a straight-line target course. How- 
ever, in plane-to-plane fire the sight will 
normally be used against a pursuit-type of 
attack course. In this case, if the time-of-flight 
setting is taken as the time-of-flight to the 
present position of the target, the generated 
kinematic lead will be in error by about 10 per 
cent. To compensate for this the time-of-flight 
setting is normally reduced by about 10 per 
cent. This tends to minimize the errors in 
kinematic lead for the pursuit-type of attack 
course. However, in doing this a sight is given 
an error of about the same amount for straight- 
line courses. This effect is typical of all types 
of fire-control equipment. 

All sight systems are sensitive in varying 
degrees to the type of attack course. As was 
pointed out earlier, the own-speed type of sight 
is very sensitive to the type of attack course. 
The lead-computing type of sight is sensitive 
to the type of attack course to a much smaller 
degree. In general it is possible to calibrate the 
time-of-flight setting of a lead-computing sight 
so that the errors in kinematic lead are min- 
imized for some particular type of attack 
course.'^^’'^^’'^® The effect of the design constants 
of the sight on its accuracy and ease of track- 
ing was the subject of an extensive study by 
The Franklin Institute.'^'^*'^®’’^® 

The various lead-computing sights were the 
subject of several assessment programs. Some 
of the analytical work on the errors of the lead- 
computing sight have been referred to previ- 
ously. The first experimental determination of 
the errors in the Mark 18 single-gyro type of 
sight was made at the University of Texas'^® 
on the testing machine developed under Section 
7.2. The testing program started at the Univer- 
sity of Texas on the Mark 18 was never carried 
very far because of the importance of getting 
performance data on the B-29 equipment. How- 


% ^KFIDEN TIAL^ 


LEAD COMPUTING SIGHTS 


197 


ever, enough information was obtained to get 
some idea of the overall performance of the 
Mark 18 sight. This test was run in such a way 
that it is difficult to make a good comparison 
between performance of the Mark 18 sight and 
other types of sights. Also, it did not take into 
account many of the psychological conditions 
which would exist in actual flying. A test under 
flight conditions in which the Mark 18 was 
compared with the K-3 and K-13 and position 
firing rule was made by Eglin Field. This was 
the first test made by the camera assessment 
method which was developed with the assis- 
tance of Section 7.2. A complete description of 
this test and the results obtained appear in an 
Eglin Field report.^^ A rather early analysis 
of the errors in the lead-computing sight when 
used against a pure pursuit course is given in 
reference 81. A summary of the various assess- 
ments made of the various types of gunsights 
available during the latter part of the war has 
been prepared.®^ This summary presents graph- 
ically the available knowledge on the magnitude 
of the errors on these various systems near the 
end of the war. A somewhat more detailed 
summary of the results of these various assess- 
ment programs was also made.*^ 

Almost at the end of the war, an electrical 
type of lead-computing sight became available 
in the European Theater. This was the K-8 
sight developed by Fairchild. It measured an- 
gular rates by means of electrical tachometers 
mounted on the gun axes. In principle it was 
similar to the Sperry sights. However, the time- 
of-flight and ballistic-lead computations were 
very accurate and in fact were more accurate 


than the accuracy of the input data warranted. 
This sight was the basis for a newer develop- 
ment which resulted in the S-3 and S-4 sights.®^ 
These sights measured angular rates by means 
of two rate gyros and had stabilized lines of 
sight. The stabilization is of the rate type which 
means that the angular rate of motion of the 
line of sight is made to be independent of the 
motion of the supporting airplane and depends 
only on the position of the control handles. In 
this system the kinematic lead-computation and 
the stabilization feature are linked together so 
that the lead computation and turret control 
are no longer independent as they are in previ- 
ous systems. This has made the over-all analy- 
sis of the errors in lead computation much more 
difficult. 

While some analysis has been done on the 
performance of the S-3 system, it is not nearly 
as complete as that for the previous sys- 
tems.®^>8® An analysis of the S-4 sight, which 
is similar except it is for a different caliber 
gun, has also been made.*^ A somewhat differ- 
ent stabilized system has been developed by 
Sperry.®® The sight is known as the S-8. It uses 
a single free gyro and provides position stabili- 
zation of the line of sight. This development is 
not yet complete but appears to be a notable 
advance in flexible gunnery fire-control sys- 
tems. 

There is no question but what the most 
promising advances in the development of the 
gunsights for flexible gunnery will be in the 
direction of stabilized systems using gyros in 
which the turret control and lead-computer are 
designed as part of the same system. 


INFIDENTIAL 


Chapter 17 


REMOTE CONTROL SYSTEMS 


17 1 NEED FOR REMOTE-CONTROL 
SYSTEMS 

W ITH THE DEVELOPMENT of the very heavy 
type of bomber, it became desirable to 
consider remote-control type of flexible gunnery 
systems. It is conceivable that such a system 
could be used to arm a large bomber in much 
the same way as the Navy uses remote-control 
systems for its main battery and antiaircraft 
armament on board ship. Locally controlled 
turrets offer a certain amount of simplicity over 
a remotely controlled system but require an 
operator for each gun position, and as normally 
used cannot put concentrated fire power under 
the control of a single gunner. On the other 
hand a remote-control system offers a great 
deal of flexibility and appears to have certain 
advantages. To date there has been no adequate 
comparative evaluation of locally controlled 
turret systems and the remote-controlled turret 
systems. The factors which favor one or the 
other system are so varied that the choice has 
been largely a function of the design of the 
particular aircraft concerned and its intended 
use. 

The main impetus during World War II for 
the development of a remote-control system was 
for the defense of very heavy bombers such as 
the B-29. Perhaps the predominant factor lead- 
ing to the choice of this system comes from the 
requirements of pressurization. Since it is un- 
desirable to pressurize the entire fuselage of a 
very heavy bomber, it is possible, using a re- 
mote-control system, to locate the sighting and 
control stations within the pressurized area 
and to place the turrets in unpressurized por- 
tions of the airplane. It is conceivable that an 
adequate locally controlled turret system could 
be developed in which certain of the turrets are 
independently pressurized. Such a scheme has 
been considered but no great effort has been 
made to develop it. 

Because of the separation of the turret and 
the sighting station in a remote-control system, 
a number of problems arise which are not 


present in the locally controlled turret. It is 
necessary to transmit accurate position data 
between various points on the airplane and to 
compensate for the effect of parallax produced 
by the separation of the sighting station and the 
turret. The separation also increases the com- 
plexity of the computer for determining the 
necessary lead. This separation also introduces 
rather serious problems in regard to the main- 
tenance of alignment and harmonization. On 
very large aircraft, this is seriously affected by 
strains in the airplane which are caused by 
many factors. On the other hand, on new high- 
speed bombers it is possible, using a remote- 
control system, to locate gun turrets where it 
would be physically impossible to locate a 
locally controlled turret. One outstanding ex- 
ample of this is the proposed installation of 
turrets on the wing tips. Another advantage of 
the remote-control system is that it is possible 
to reduce considerably the size of that portion 
of the turret which is exterior to the normal 
surface of the airplane. This is important in 
reducing the drag due to the turrets and is most 
important in the case of new high-speed air- 
planes. 

17 2 EARLY DEVELOPMENTS 

The development of remote-control systems 
started before the United States entered the 
war, with the initiation of the development 
of a completely automatic radar system for 
gunlaying. When the first contract for such a 
system was let, the necessity for a suitable com- 
puter was not appreciated. The system consisted 
only of one or more radar sighting stations 
which pointed one or more remotely con- 
trolled gun turrets. It was pointed out by 
Section 7.2 (then Section D-2) that for all- 
round firing it was absolutely necessary to 
provide a suitable computer as part of this 
system in order to get any firing accuracy at 
all. This original development for a complete 
radar gunlaying system, known as AGL, was 
carried on by the General Electric Company^^-^^ 


QOXFlDEyTlAL } 


198 


GENERAL ELECTRIC SYSTEM 


IQQ 


with the cooperation of the Radiation Labora- 
tory at MIT. The system was known as AGL-1. 
The AGL-1 system was obsolete before it was 
ever finished and was never tested. However, it 
formed the basis for the development of the 
manually operated remote-control system which 
was finally used operationally in the B-29’s over 
Japan. In fact, while this AGL-1 system was 
never produced or used, it made some of the 
most important contributions to the use of 
radar in airborne fire-control systems and to 
the general development of computers for such 
systems. 

Before long a number of developments on re- 
mote-control systems were under way. Most of 
these were for the purpose of providing com- 
pletely automatic radar tracking and ranging 
and multiple operation of remotely controlled 
turrets. An early report on these various sys- 
tems is reference 89, which describes all the 
important remote-control systems which were 
under development during World War II, with 
the exception of a Westinghouse system which 
was not developed until the latter part of the 
war. During the early part of the war there 
was great interest in developing these com- 
pletely automatic systems. The concentration of 
such a great amount of effort on completely 
automatic fire-control radars for aircraft use 
resulted in a delay in the simpler radar systems 
which were eventually found to be of much 
greater practical use. In fact it was not long 
before interest in the completely automatic 
systems decreased to almost nil and the effort 
was concentrated on the simpler fire-control 
radars, which will be discussed later. 

3 general ELECTRIC SYSTEM 

The main contribution of this early develop- 
ment was the ground work that it laid for the 
development of computers for remote-control 
systems. The only remote-control system which 
saw use during the war was the General Elec- 
tric system installed in the B-29 airplane.^^-^^’^^ 
This system is manually operated and except 
for a few installations at the end of the war 
made no use of radar. Because of the im- 
portance of this system, considerable effort was 
exerted in determining its performance by test 
and analysis and in increasing its accuracy. 


References 95, 96, and 97 give a good descrip- 
tion of the theory of the operation of this 
system. This study was brought about by the 
fact that the system, as originally produced, 
did not have sufficient accuracy and was un- 
satisfactory in many ways. 

Modifications for improving the GE system 
were almost continuously under development. 
The remotely controlled turrets of the GE system 
were of excellent design and gave exceedingly 
good service. The data transmission system 
which was used was very accurate and con- 
tributed negligible error to the overall opera- 
tion. In fact it can be said that the turret and 
data transmission system design was entirely 
satisfactory. The computer which was finally 
produced was large and complicated and could 
not be considered as entirely satisfactory. It 
was not the only computer designed under de- 
velopment by GE but was chosen because it 
promised to be the computer which could most 
easily be put into production and meet the 
rather rigid time schedules. It is very probable 
that if the choice of a computer could have been 
delayed another six months a considerably im- 
proved computer would have resulted. 

The most unsatisfactory component of the 
General Electric B-29 system was the sighting 
station. This was a pedestal-type sight which 
was operated directly by the gunner without 
benefit of power controls. It was awkward to 
handle both for ranging and tracking. It re- 
quired extensive training and practice in its 
use and even then the tracking and ranging 
errors were excessive. In the preproduction 
model kinematic lead was computed by means 
of a free gyro which was contained in the sight 
head. This gyro was processed by electrical 
means so as to remain parallel to the optical 
line of sight. The servo system used for pro- 
ducing this precession was operated by a set 
of contacts mounted on the gyro and the sight 
case. The biggest difficulty resulted from the 
use of these contacts in the servo systems. An- 
other serious difficulty encountered was an in- 
stability which made it impossible to use a single 
gyro. This could be overcome only by providing 
two separate gyros at the sighting stations. The 
sight actually put into production was the two- 
gyro sight. Another serious difficulty which 
never was overcome satisfactorily was the sen- 


|[cONFIDEN TIAir^ 


200 


REMOTE-CONTROL SYSTEMS 


sitivity of the system to the character of the 
tracking errors. 

This latter difficulty was realized very soon 
after the first systems were put into operation 
and steps were taken to develop a more suitable 
sighting station. The first such improved sight- 
ing station resulted in what was known as the 
free-gyro lead computer. This consisted of an 
entirely new sighting station containing a 
single free gyro. Only minor modifications were 
required in the computer to adapt the system 
to its use. This free-gyro computing system 
(described in detail in reference 98) was given 
fairly extensive tests and gave an accuracy of 
performance which was substantially greater 
than that of the standard system. By the time 
the war ended, plans were already under way 
for producing this free-gyro system in quan- 
tity and eventually replacing the standard sys- 
tem with it. 

A second improvement was started much 
earlier than the free-gyro system. This is the 
development of a gyro-stabilized sight^^ having 
power control. This gyro-stabilized sight pro- 
vided much more accurate lead computation and 
also provided tracking and ranging controls 
that were a very great improvement over either 
the standard system or the free-gyro system. 
This sight promised to be considerably better 
than that of the standard B-29 system or the 
free-gyro sight. However, in spite of this the 
development of the gyro-stabilized sight was 
considerably slower than that of the free-gyro 
sight. This is largely due to the lack of any 
strong central planning group within the Air 
Force which could competently evaluate the 
various proposals for the development of air- 
borne fire-control equipment and which could 
decide on which line of endeavor to follow. The 
gyro-stabilized sight promised to eliminate all 
the serious difficulties that were encountered 
with the standard system and yet the effort put 
on its development was exceedingly small. Per- 
haps if adequate assessment devices had been 
available earlier in the war, this would have 
helped to direct GE’s efforts into more fruitful 
channels. 

Even after the standard B-29 fire-control sys- 
tem was in production and installed in operat- 
ing airplanes, its operation was still not entirely 
satisfactory. As a result a number of studies 


were made to eliminate the major difficulties. 
The portions of the computer which determine 
the ballistic lead and the corrections necessary 
on account of parallax did so with an accuracy 
which was considerably greater than was neces- 
sary. In fact one major criticism of the stand- 
ard B-29 computer was the poor design balance 
between the kinematic lead computer and the 
ballistic lead and parallax computers. The two 
most important difficulties were the awkward- 
ness of the pedestal sight as a tracking device, 
which made it very hard to track and range 
satisfactorily, and the rather large time lag 
inherent in the computer, which seriously af- 
fected the computation of the kinematic lead. 
The time lag introduced by the computer in the 
computation of the kinematic lead was most 
serious in the case of nose attacks. Such attacks 
proved to be rather popular with the Japanese 
and this made it even more important to im- 
prove the performance of the standard com- 
puter. Studies and recommendations on improv- 
ing the standard B-29 computer were made by 
the Applied Mathematics Group at Columbia. 
Their results are given in a series of re- 
ports.^®^'^^^ 

At the time that the Army Air Force decision 
was made to freeze the development work and 
get the present B-29 computer into production. 
Section 7.2 contracted with GE to continue the 
computer development work. The Section felt 
that there was a good possibility of producing 
a new computer which was considerably supe- 
rior to the standard computer. This was par- 
ticularly true since at the time the production 
design was decided on, GE had not completed 
any developmental computer nor had an oppor- 
tunity to test and study such a computer. In 
fact the development of the gyro-stabilized 
sight was a direct outcome of this continuing 
development work under NDRC. The computer 
which GE was developing for Section 7.2 was 
not quite completed at the time the contract 
had to be terminated because of the end of the 
war. However, enough work has been done to 
indicate that this new computer was consider- 
ably superior to the standard B-29 computer. 
This new computer will undoubtedly be com- 
pleted by GE under the direction of the Army 
Air Forces. Perhaps the most important con- 
tribution which was made through its develop- 




1 


ONFIDENTIAL 


SPERRY SYSTEMS 


201 


ment was the design of a second new computer 
which was considerably smaller and less 
complicated than any previous one. 

17.^ EVALUATION OF GE SYSTEM 

The standard B-29 fire-control system was 
first tested by the Army Air Forces Proving 
Ground Command in Eglin Field. This is the 
first test in which official recognition was given 
to the fact that this system was not entirely 
satisfactory in its operation. This particular 
test and the conclusions drawn from it are 
given in a report of the Army Air Forces 
Board.^®^ While this test served to stimulate 
considerable effort for the purpose of improv- 
ing the operation of the standard B-29 system, 
it cannot be considered as a particularly re- 
liable evaluation of the fire-control system. 
Plans were eventually made for re-evaluating 
the B-29 system by means of a satisfactory 
method, but for various reasons these plans 
were never carried out. In fact no completely 
satisfactory evaluation of the B-29 fire-control 
system has ever been made. 

Under directive AC-92 from the Army Air 
Forces, the Applied Mathematics Panel of 
NDRC undertook to make a rather extensive 
and elaborate tactical evaluation of the B-29. 
The principal part of this work was carried out 
by the University of New Mexico in Albu- 
querque. The re-evaluation of the B-29 fire- 
control system by Eglin Field was a part of 
this program. However, the New Mexico group 
found it necessary to run some tests on the 
accuracy of the system. The results of this test 
are given in one of their reports.^®® The whole 
AC-92 program was intended to be a quick and 
not too thorough study of use of the B-29, 
and the test run by the New Mexico group on 
the accuracy of the fire-control system was 
carried out with this in view. As a result this 
test can be taken only as an indication of the 
general accuracy of the B-29 system and can- 
not be considered as being particularly reli- 
able. 

Toward the end of the war the University 
of Texas Testing Machine, which will be dis- 
cussed later, became available and was used 
quite extensively in testing and studying the 
B-29 system. The problem of defending the 


B-29 against nose attacks was so critical that 
the problem of improving the performance of 
the computer for such attacks was given first 
priority. All the important proposals for mod- 
ifying the computer were studied^®^ and ad- 
ditional tests were run.^^^^ Eventually the Uni- 
versity of Texas Testing Machine was used to 
make a comparison of the standard B-29 sys- 
tem with the free-gyro sighting system and the 
stabilized sighting system. The results of these 
studies as well as those previously mentioned 
are discussed in reference 109. 

Toward the end of the war the General Elec- 
tric Company developed an excellent assessment 
facility at Brownsville, Texas, and succeeded 
in running some adequate tests on the standard 
B-29 system and some of its modifications. No 
report is available on the results of this test 
but the proposed program is described.^®® 

5 SPERRY SYSTEMS 

Although the General Electric Company de- 
velopments were the ones which were finally 
accepted by the Army Air Forces and put into 
production, there were other developments of 
remote-control systems which might possibly 
have been superior to the GE system. The most 
important of these is a series of developments 
by the Sperry Gyroscope Company. Very early 
in the war, Sperry undertook to develop a 
completely automatic radar gunlaying system 
using remote-control turrets. The computer 
which was used in the first phase of this radar 
fire-control system was the Sperry P-4 com- 
puter. This computer was an adaptation of the 
Sperry K-3 and K-4 sights to the central sta- 
tion type of computer. The sight station was a 
double ended periscope mounted directly on 
the computer. The periscope was power con- 
trolled from a pair of handle bars and made 
use of aided tracking. The remotely controlled 
turrets developed by Sperry were very ac- 
curately positioned by means of a selsyn data 
transmission system and a hydraulic turret 
servo. 

There were several serious objections to the 
P-4 computer. The field of view of the periscope 
was only 30 degrees and this made it virtually 
impossible to carry out a search operation with 
the periscope alone. This eventually led to the 


202 


REMOTE-CONTROL SYSTEMS 


development of what was known as a presight- 
ing station which consisted primarily of a ped- 
estal-type sight that could be pointed directly 
by an operator. This sight was pointed at a 
target as soon as it was picked up and the in- 
formation automatically relayed to the com- 
puter, which resulted in automatically putting 
the line of sight of the periscope almost on the 
target. Preliminary tests indicated that this 
system was very successful. Perhaps the most 
fundamental objection to the P-4 computer was 
the fact that, like the K-3 and K-4 sights, it 
measured angular rates with respect to the 
bomber. This introduced serious errors into 
the computation of kinematic lead when the 
bomber takes evasive action. A lesser difficulty, 
but one which is still fundamental, is due to 
the fact that the P-4 computer did not correct 
for parallax between the sighting station and 
the turret and contained rather substantial 
errors as a result of not properly carrying out 
the various required axis conversion. 

The P-4 computer was in production very 
early in the war and could have been used long 
before the General Electric system for the 
B-29 was actually in production. At the time 
this Sperry system was developed there was no 
really adequate means of assessing it so that 
the importance of the various known theoretical 
errors was never fully evaluated. It is very 
probable that like the K-3 and K-4 sights, which 
were eventually tested, the Sperry central fire- 
control system would have been found to be at 
least as adequate for the defense of the B-29 
as the standard GE system. The P-4 computers 
which were produced were never used. A de- 
scription of this complete system will be found 
in the preliminary instructions for it which 
were prepared by Sperry.^^^ 

The first phase of the complete radar gunlay- 
ing system developed by Sperry was essentially 
the central fire-control system just discussed 
with the addition of a completely automatic 
X-band radar. In this first-phase system the 
position data obtained by the radar was used 
to provide a target on a cathode-ray tube which 
was tracked by the gunner who operated the 
control handles of the P-4 computer. It was 
realized at the time that this arrangement 
would probably not be particularly satisfactory 
and that the accuracy of the P-4 computer left 


much to be desired. However, this first-phase 
system was the first complete remote-control 
system to be completed and flown and could 
have been used to provide some very useful 
information on the general technical value of 
such a system. Such a study was never carried 
out primarily because the AAF decided to con- 
centrate on the development and production of 
the GE system and the Sperry system never 
was given very serious further consideration. 
This first-phase AGL system is described in a 
Sperry report.^^^ 

At the same time that the first phase of the 
Sperry central fire-control system development 
was being finished, work was started on the de- 
sign and development of a completely new com- 
puter which was to be a part of a final-phase 
system, and on the modification of a P-4 comput- 
er for use in an intermediate-phase system. The 
modified P-4 computer would be associated with 
a single free gyro which would be a part of the 
kinematic lead computer, and would also serve to 
stabilize the line of sight. This single-gyro 
system would eventually be made a component 
of the final-phase computer. The intermediate 
phase development was completed about a year 
before the end of the war and was given rather 
extensive tests by Sperry. Within the limita- 
tions of the P-4 computer, which still contained 
some of its fundamental errors, this interme- 
diate-phase system proved to be very accurate 
and easy to handle. This particular system was 
never tested by the AAF. In fact, when the 
development had been completed, all further 
work on such systems by Sperry was stopped. 
A complete description of this intermediate- 
phase system and the tests which Sperry ran 
on it are contained in one of their reports.^^^ 
The design of the computer for the final-phase 
system was completed by Sperry but no parts 
were made. At the same time a double periscope 
having a 70-degree field was developed and 
built which eliminated most of the objections 
to the original double periscope. A brief descrip- 
tion of this final-phase computer design is also 
contained in the report just mentioned.^^^ 

OTHER SYSTEMS 

The difficulties which were encountered with 
the standard GE computer for the B-29, and 


OTHER SYSTEMS 


203 


which delayed its production almost a year, led 
NDRC to start another central station com- 
puter development by means of a contract with 
the Fairchild Camera and Instrument Com- 
pany. This particular development was to be 
based on the Fairchild K-8 lead-computing sight 
which already was beginning to go into produc- 
tion. The Fairchild computer was almost en- 
tirely electrical in nature and used two rate- 
type gyros for the computation of kinematic 
lead. The computer, as finally designed, was 
mounted in the same case as the standard B-29 
computer and was interchangeable with it ex- 
cept for the gyros in the sighting station. Be- 
cause of the different type of kinematic lead 
computation, the two GE gyros had to be re- 
placed by the two Fairchild gyros for use with 
the Fairchild computer. One model of this com- 
puter was completed but never tested. A the- 
oretical consideration of the Fairchild computer 
design would indicate that it would compare 
very favorably in performance with the stand- 
ard GE computer. A good description of this 
computer development is given in the Fairchild 
final report to NDRC.^^^ Very late in the war 
one other central station computer develop- 
ment was started. This was carried out by 


Westinghouse and brought to the point where 
one computer and sighting station were avail- 
able for test. This Westinghouse system used a 
gyro type of kinematic lead computer and pro- 
vided stabilization of the line of sight. 

The British were interested in remote-control 
systems but did not undertake to develop any- 
thing so elaborate as any of the American sys- 
tems. They developed an excellent remotely 
controlled 20-mm turret and data transmission 
system but made no attempt to develop a central 
station type of computer. The computer which 
they used was a Mark II-c type of lead-com- 
puting sight which was mounted so that it 
could be operated by power control from a pair 
of handle bars. The computed gun position 
determined by this sight was then relayed to 
the remote-control turret through a simple 
mechanical type of parallax computer. A dis- 
cussion of this system and its performance will 
be found in two British reports from the Royal 
Aircraft Establishment, Farnsborough“^‘“^ It 
is interesting to note that largely as a result 
of this work by the British the Americans be- 
came interested in trying the same sort of an 
arrangement in the B-29. However, this was 
never carried out. 



Chapter 18 


TRACKING AND RANGING 


18 1 GENERAL DISCUSSION 

T he most important operation which is 
carried out by any fire-control system is 
that of accurately locating the position of the 
target. In all airborne fire-control systems, this 
is done in terms of a spherical coordinate sys- 
tem. This means that the data on the target 
position is given in terms of th*e distance to 
the target, which is called range, and the ele- 
vation and azimuth bearing angles of the tar- 
get. The process of operating the direction- 
finding equipment with which the angular po- 
sition of the target is determined is known as 
tracking. Operation of the range measuring 
equipment is known as ranging. While it would 
be more appropriate to refer to these operations 
as angle tracking and range tracking, the pre- 
vious terms are very well established and have 
come to have the meanings given. 

The simplest form of tracking in fiexible 
gunnery occurs in the use of the fiexible gun 
such as is found at the waist positions of a 
bomber like the B-17. In this case there is no 
range-measuring device other than a set of 
stadia rings in the fixed sight. Tracking is ac- 
complished by manually moving the gun about 
without the aid of any power control. Such 
control is known as direct control. The ac- 
curacy of tracking with a flexible gun mount 
such as this is extremely poor. One of the im- 
portant factors that contributes to this inac- 
curacy is the large mechanical load which the 
gunner must overcome due to the weight of the 
gun and the various aerodynamic forces on it. 
The first step in improving the tracking ac- 
curacy of the gunner was to mount the gun 
in a power-driven turret. This permitted the 
use of more than one gun and allowed the op- 
erator to ride around in azimuth with the gun. 
The power required to move the gun and the 
turret is supplied by a motor which is controlled 
by the position of some sort of a control handle. 
In the common turrets, a pair of control handles 
was used which adjusted the speed of the motor 
driving the turret. The usual arrangement was 


to have the motor drive produce an angular 
rate in the gun position which was approxi- 
mately proportional to the displacement of the 
control handles. This type of control is known 
as rate control. 

For practical reasons the turret was normally 
mounted so that it rotated in azimuth about the 
vertical axis. The guns which were mounted in 
the turret were arranged so that they could be 
rotated in elevation about a horizontal axis 
carried on the turret. The control handles ro- 
tated about a similar pair of axes and the dis- 
placement of the handle bar about these axes 
controlled the rate-of-motion about the cor- 
responding axes of the gun turret. Such a turret 
arrangement is referred to as a cylindrical tur- 
ret. This type of turret was the most common 
type to be used during this war. In some cases, 
a turret was so arranged that it rotated both 
in azimuth and in elevation, and carried the 
gunner and the guns with it. This type of tur- 
ret is known as a spherical turret. In this case, 
also, the displacement of the control handles 
determine the rate-of-motion of the turret and 
gun about the two axes of rotation. A descrip- 
tion of all the standard turrets used during 
World War II will be found in the AAF Tech- 
nical Order series, 11-45, on aircraft turrets. 

Experience showed that even with power- 
driven turrets using rate control, the tracking 
accuracy obtained was not satisfactory. The 
ability of a gunner to track accurately with 
such a system depends on many factors such as 
the amount and quality of his training, the type 
of target course being followed, the design 
constants of the control system and the number 
and type of other functions the gunner has to 
carry out simultaneously with the tracking. 
Among these other functions are such things 
as ranging, identification of the target, opera- 
tion of the trigger and various control switches. 

The method usually used for measuring the 
target range was the stadiometric method. This 
is accomplished by adjusting the size of the 
reticle until it bracketed the target, of assumed 


CONFIDENTIAI^ 


204 


TRACKING AND RANGING STUDIES 


205 


size. From the assumed target size and the 
known size of the reticle, the range of the tar- 
get could then be determined. This was ac- 
complished in the mechanism controlling the 
reticle size so that the computed target range 
was continuously available and inserted into 
whatever computer was making use of such in- 
formation. The range obtained by this stadio- 
metric method was usually very inaccurate. In 
fact, in any of the lead-computing systems 
which made use of range data, the greatest in- 
accuracies in the computed lead were those due 
to the ranging errors. 

There were two general ways in which the 
target’s position data could be improved in ac- 
curacy. The first of these was to improve the 
tracking and ranging controls and the training 
of the gunner so that the system as a whole 
could be used with greater accuracy. The second 
of these was to replace the manually operated 
range and tracking system by one which was 
automatic in either tracking or ranging, or 
both. This could be accomplished by the use of 
radar and some systems were developed for 
doing it. This will be discussed later. 

18 2 tracking and ranging studies 

To improve the accuracy of the manually 
operated system. Section 7.2 undertook a num- 
ber of studies on tracking and ranging. The 
most important of these was carried out by The 
Franklin Institute in Philadelphia. The Frank- 
lin Institute developed mechanisms for simu- 
lating the dynamics of various types of tracking 
controls and of the standard lead-computing 
sights which were to be used with them. A gen- 
eral summary of the work carried out on the 
tracking study at The Franklin Institute will 
be found in their final report on this study.^® 

The first part of the study was carried out 
using a mechanical device for simulating the 
turret tracking control and the lead-computing 
sight. One objective of this study was to evalu- 
ate the use of aided tracking control on a turret. 
This type of control consists of a combination 
of the usual rate control and of direct control. 
A second objective of the study was to deter- 
mine the best choice of the design constants for 
the lead-computing sight. The first results of 
this work are given in a report made in August 


of 1943.^1^ The most outstanding result was the 
conclusive evidence that aided tracking control 
was substantially superior to rate control. 
Further work substantiated this and was re- 
ported to the Services soon thereafter.^^® Ad- 
ditional work^^® was done using the mechanical 
simulator with a considerably greater variety 
of control constants and lead-computing sight 
constants. 

In any fire-control system the gunner must 
decide when to fire and when not to fire. In 
general, he should withhold his fire until the 
target is within suitable range and then should 
fire only when he feels that his guns are pointed 
with sufficient accuracy to get effective hits. 
When using a lead-computing sight, his only 
available method is to fire when he considers 
that his sight is accurately pointed at the tar- 
get. A study was carried out to evaluate the 
gunner’s ability to judge when to fire and when 
not to fire. The results of this study are given 
in two extensive reports.^20.121 The general 
conclusion reached is that the gunner’s judg- 
ment of when to pull the trigger is quite un- 
reliable. This is due to the fact that the gunner’s 
judgment of his tracking error is very poor 
and also to the fact that with a lead-computing 
sight the intervals during which the tracking 
error is small is not necessarily those during 
which the gun error is small. 

As has been indicated, the early work on 
tracking which was done at The Franklin In- 
stitute made use of a mechanical simulating 
mechanism. With this device it was possible to 
study only target courses having constant or 
variable angular rates at constant range. Such 
target courses are quite different from those 
actually found in practice. This was brought 
about due to a physical limitation contained in 
the design of the mechanical simulator. Since 
the use of such unrealistic courses in the study 
might have some inffuence on the final result, a 
new simulating mechanism was built on which 
realistic courses could be used. This mechanism 
was largely electrical in nature and somewhat 
more accurate in performance than the mechan- 
ical simulator. It also provided for a much 
greater variety of tracking-control constants 
and lead-computing sight constants. Studies on 
the electric simulator verified the results of the 
previous work and gave additional information 


confidentia; 


206 


TRACKING AND RANGING 


on the best choice of tracking-control constants 
and lead-computing sight design. Three reports 
on these results have been prepared. 

On all the work previously mentioned, the 
complete turret control and the lead-computing 
sight were simulated with the gunner remain- 
ing stationary. In an actual turret system the 
gunner is subjected to certain forces as a result 
of the motion of the turret in which he rides. 
Since this effect had not been considered in the 
previous studies, it was decided to continue the 
work using a system involving an actual turret. 
This was done and the results of that study 
have been reported. An analysis of the work 
using the turret system was made to obtain ad- 
ditional data on the optimum tracking-control 
and sight constants.^^^ 

One additional factor, which was considered 
in these studies was the effect of training and 
practice. All through the work a statistical eval- 
uation of the results was made to be sure that 
the conclusions regarding the tracking controls 
and the lead-computing sight constants were 
not unduly affected by variations in the sub- 
jects used in the study. A special study 1^4 ^^s 
made to determine the effect of practice. It is 
interesting and somewhat discouraging to note 
that in spite of the fact that very early in the 
war the tracking studies at The Franklin In- 
stitute showed the superiority of aided track- 
ing over velocity tracking it was not until very 
near the end of the war that any turrets were 
produced with aided tracking control. 

With the development of the University of 
Texas Testing Machine another source of in- 
formation on the accuracy of tracking became 
available. The main objective of this machine 
was to evaluate the overall performance of a 
flexible gunnery system. However, in the 
process of carrying out this evaluation, data on 
tracking and ranging accuracy also became 
available. The first data of this sort which was 
obtained at the University of Texas will be 
found in their report on the Mark 18 gun- 
sight."^® While the work at The Franklin Insti- 
tute was entirely on tracking, the studies at the 
University of Texas were on both tracking and 
ranging. Before any extensive studies could be 
made on lead-computing sight systems, the B-29 
central fire-control system became of greater 
importance. As has been previously mentioned. 


the accuracy of tracking with the GE pedestal 
sight was quite unsatisfactory. As a result, a 
series of tests on this system were undertaken 
by the University of Texas. The first results 
on tracking with the GE sight appear in an 
early report.^^^ Additional data were accumu- 
lated on the studies of the overall accuracy of 
the GE system, which have been previously 
mentioned.^^^’^^®’!^^ 

The University of New Mexico also ac- 
cumulated a large amount of data on tracking 
and ranging accuracy. One of their reports,^-® 
deals with the use of the K-3 sight mounted in 
a standard Sperry turret. Another^®^ is con- 
cerned with tracking accuracy obtained with 
the GE B-29 system. Of all the studies thus 
far mentioned, only those at The Franklin In- 
stitute were sufficiently extensive to give any 
useful information on the choice of constants 
for the systems considered. A considerable 
amount of additional tracking information is 
available in the various tests conducted at the 
Army Air Forces Proving Ground Command, 
Eglin Field, Florida and at the Armament Test 
Section of the Naval Air Station, Patuxent 
River, Maryland. In both of these places the 
general objective of the the tests was the evalu- 
ation of the overall performance of the various 
systems and as a result there was very little 
analysis of tracking data. The one important 
exception is an analysis of the Eglin Field 
data.12® 

STABILIZATION 

It has already been pointed out that the use 
of aided tracking control gives considerably 
better performance in tracking than the stand- 
ard type of rate control. An additional improve- 
ment in the performance of manually operated 
tracking systems can be had by the use of 
stabilization. It is known that with the ordinary 
tracking-control system the accuracy of track- 
ing is substantially reduced by the influence of 
the motion of the gunner’s platform. This 
means that tracking accuracy obtained while a 
bomber is carrying out maneuvers or evasive 
action is much poorer than when the bomber is 
flying a straight and level course. This is prin- 
cipally due to the fact that under conditions of 
evasive action the gunner operating the track- 


\x)NFIDENTIAi\ 


RADAR FOR GUNLAYING 


20T 


ing controls has not only to produce turret or 
sight motions which correspond to the motion 
of the target, but must also produce turret and 
sight motions which compensate for the motions 
of the bomber. The problem of compensating 
for the bomber’s motion makes the tracking 
problem sufficiently more difficult so that the 
resultant accuracy decreases very greatly. By 
the use of a single or double gyro in the turret- 
control system, it is possible to arrange the con- 
trols so that the motions of the bomber are auto- 
matically compensated. This leaves the gunner 
with only the problem of providing the motions 
which are necessary to track the target. 

The first stabilized turret control was de- 
veloped very early in the war by the Ford 
Instrument Company. This turret was intended 
to be installed in the nose position of a Navy 
flying boat. Mainly because of its excessive 
size and weight this turret was never produced. 
It was subsequently improved by the Ford In- 
strument Company but only a few of these 
improved versions were ever built. The pre- 
liminary tests on the stabilized turret showed 
the great advantages to be gained by the use 
of stabilization. Following this Navy develop- 
ment there was no very serious effort to develop 
stabilized tracking controls until fairly well 
along in the war. This is surprising in view of 
the rather definite improvements to be gained. 

Sperry developed a stabilized spherical turret 
for use in the nose and tail of the B-32. A num- 
ber of these turrets were actually produced but 
very few of them were put into use. Sperry also 
undertook to develop a stabilized spherical tail 
turret which was to be used with the S-8 sight- 
ing system. In this turret the gyro which pro- 
vides stabilization is also the gyro which is used 
for the computation of kinematic lead. This 
arrangement is one which is to be expected for 
future stabilized sighting systems. The Sperry 
S-8 sight system also provides for automatic 
S-band radar. Fairchild also developed a stabi- 
lized-control system in conjunction with the 
development of their S-3 sight. Both the Sperry 
and the Fairchild systems were still in develop- 
ment at the end of the war. As has already been 
mentioned, the General Electric Company had 
under development a completely stabilized sight 
for use with their B-29 fire-control system.®^ 
The first stabilized sighting system produced 


by Sperry was that used in the intermediate 
phase of their AGL development. This system 
was given rather extensive tests by Sperry al- 
though it was never flown or tested by the AAF. 
The Sperry system also made use of aided 
tracking control. Considerable tracking data is 
available in the Sperry report^^^ as well as a 
number of comparative results showing the 
relative advantages of stabilization. 

4 RADAR FOR GUNLAYING 

During the war a tremendous amount of 
effort was put on development of various types 
of airborne radar sighting systems. The first 
developments were by Sperryi^^'^^^ Gen- 
eral Electric.®^ In both of these systems the 
objective was to provide completely automatic 
position finding by means of radar. This was 
accomplished satisfactorily from the point of 
view of performance in both of these develop- 
ments. However, for a number of reasons, the 
principal ones being size and weight, these 
systems were never used. 

Fairly early in the war it became apparent 
that these completely automatic radar equip- 
ments were for use only on very heavy bombers 
and, therefore, were for use considerably in 
the future. As a result, the available effort was 
shifted from these systems to the development 
of very lightweight radars which could be used 
on existing aircraft. Since one of the greatest 
sources of error in the use of lead-computing 
sight systems was contributed by the very in- 
adequate ranging performance obtained, con- 
siderable effort was made to develop a suitable 
radar ranging set. The first production model 
of this range set was the AN/APG-5. This set 
is described in a Navy operating manual pre- 
pared by the Radiation Laboratory.^^o Only a 

relatively small number of these sets were pro- 
duced and these were entirely for experimental 
purposes. 

Perhaps the biggest problem in providing 
radar range for use with flexible gunnery sys- 
tems was that of finding suitable space for the 
installation of the radar set. This problem was 
not as severe in the case of fixed gun fighters 
and at the end of the war there were a number 
of experimental fighter systems under test 
which made use of the AN/APG-5 set for 


208 


TRACKING AND RANGING 


automatic ranging. While a number of tests 
were made on fire-control systems using this 
radar set, no really reliable test information 
has been provided. Tests on radar ranging sets 
of the type AN/APG-5 indicate that the ac- 
curacy of range data obtained is entirely sat- 
isfactory. However, some difficulties often arise 
in the use of this set if there is more than one 
target in the field. This difficulty can be largely 
overcome by suitable training. Another factor 
in the use of radar ranging devices is that the 
use of accurate range may under some cir- 
cumstances decrease the accuracy of the fire. 
This occurs when the systematic errors which 
are present in any computing system, are of 
about the same size or larger than the tracking 
errors. In such a case the use of accurate range 
may result in systematic misses, whereas with 
the use of manual ranging the dispersion of the 
ranging errors is sufficiently great to provide 
enough overall dispersion in the gun position 


to give at least some reasonable probability of 
getting hits. This means that accurate ranging 
data can be effectively used only when the com- 
puting system is properly calibrated. This effect 
has been amply demonstrated both analytically 
and experimentally. 

The only radar set for aerial gunnery to be 
produced in any quantity was AN/APG-15B. 
This is described in an instruction manual pre- 
pared by the Radiation Laboratory. This set 
provides not only automatic range information 
but an angular position indication which may 
be used for manually tracking the target. This 
set was eventually installed in the tail position 
of a number of B-29s which were sent to the 
Pacific Theater. 

A rather good summary of the various fire- 
control radars available or under development 
at the end of the war has been prepared by the 
Armament Section of the Assistant Chief of 
Air Staff-4.^®^ 


\ CONFIDENTIAL | 


Chapter 19 


SIMULATION AND GUNNERY ASSESSMENT 


i ASSESSMENT METHODS AND 
SIMULATION 

A t the beginning of World War II, there 
- was no adequate method and no suitable 
equipment available for adequately evaluating 
the performance of flexible gunnery systems. 
The usual test for determining the performance 
of such systems was for combat experienced 
gunners to use it by shooting at towed-flag tar- 
gets. The quality of performance of the system 
was then judged by the percentage of hits ob- 
tained on the flag target. This method of test 
was later shown to be very inadequate. The 
usual experiment was not done under suitably 
controlled conditions, the gunners used were of 
unknown ability and training and the number 
of hits obtained on the target was usually so 
small as to give no reliable indication of the ac- 
curacy of shooting. In addition, the quality of 
performance was based largely on the gunner’s 
opinion of the system under test. 

One of the most important jobs which Section 
7.2 did during the war was to assist in the 
establishment of suitable methods of assessing 
flexible gunnery systems and in the develop- 
ment of the necessary equipment. The Section 
was also largely responsible for educating the 
Army and the Navy in the general philosophy 
of quantitative experimental work. 

There are several general methods that can 
be used for evaluating aerial gunnery systems. 
One such method is to study the equipment 
analytically and to compute its performance 
numerically. The main objection to this method 
is that it is impossible to take into account all 
the factors which influence the performance of 
such a system. This method is most useful in 
determining the performance of a system under 
assumed ideal conditions. It also has the ad- 
vantage that it provides a means of breaking 
down the overall error into its component parts, 
and of determining the sources of the various 
parts of the error. This method was applied 
rather extensively to an analytical evaluation 
of the more common lead-computing sight 


systems. The work was carried out by the Ap- 
plied Mathematics Group at Columbia Univer- 
sity under the direction of the Applied Mathe- 
matics Panel. This work was known as Study 
104 on The Analytical Assessment of Certain 
Lead Computing Sights. A large number of 
reports resulted and most of these have already 
been referred to under the sections of this re- 
port pertaining to the particular sighting sys- 
tem. 

A second method of assessment is that of 
simulation. In this method the system under 
study is represented by a model or simulator 
which is then subjected to the various assess- 
ment experiments. The principal use of this 
method was in the various tracking studies con- 
ducted under the direction of Section 7.2. The 
tracking studies carried out at The Franklin 
Institute used such simulators and have already 
been discussed. The three simulators which 
were used in that study are described in three 
reports by The Franklin Institute.^^2,133,134 

In any study of a gunnery system, the oper- 
ator, or gunner, plays a very important part. 
It is very important that the errors in the over- 
all performance of the system contributed by 
the gunner be known. In fact one of the most 
difficult problems in such assessment work is 
to design the experiment in such a way that 
the effect of the gunner’s performance can be 
evaluated. In carrying out experiments with 
various types of simulators, it would be very 
desirable to have some sort of an artificial 
gunner. Some attempt was made to determine 
the general dynamic properties of a typical 
gunner which then could be built into an artifi- 
cial gunner. While such work did not progress 
very far, enough was done to indicate the 
future possibilities. The earliest work appears 
to have been done in England.^^^ The analysis 
of the dynamics of a human being was based 
on the use of sinusoidal courses of varying 
frequencies. The method of analysis used is that 
so commonly applied by electrical engineers. A 
similar but somewhat briefer study was made 




confidentia: 


209 


210 


SIMULATION AND GUNNERY ASSESSMENT 


by Columbia University using a slightly dif- 
ferent technique of the electrical engineer. In 
this case the courses used for analysis were of 
the transient type. This work is described in 
the final report of the Columbia University 
project.^^® 

19.2 UNIVERSITY OF TEXAS TESTING 
MACHINE 

In addition to the two methods of assessment 
just described there are several entirely ex- 
perimental methods which can be used to evalu- 
ate a complete gunnery system, including the 
gunner. One obvious such method is some form 
of flight test. This leads to certain practical dif- 
ficulties which are present in any flight test. 
Even if the experiment is properly designed so 
that all the necessary factors are controlled, 
there are always the difficulties due to the in- 
operability of airplanes, the effects of weather, 
and the rather large time and cost involved. 
These difficulties can be largely overcome by 
the use of a device on the ground which will 
allow the use of a full-size gunnery system and 
provide the gunner with reasonably realistic 
target courses. The desirability of such a test- 
ing machine was pointed out early in the war by 
Section 7.2 (then Section D.2).i^^ At the same 
time the general specifications for such a 
machine were also prepared. Both the Army 
and Navy agreed to the desirability of such a 
ground testing machine for evaluating per- 
formance of flexible gunnery equipment, and 
the development of such a machine was carried 
out by Section 7.2 at their request. The work 
was done at the University of Texas and the 
machine developed by them has come to be 
known as the Texas Testing Machine. A very 
large amount of effort was put into its develop- 
ment and a great many proposals were studied 
for its design. 

It was originally intended to build a machine 
which projected target spots onto a large 
screen which could then be followed by the 
gunner operating the equipment under test. 
On the basis of experience with such devices 
which had been obtained with the Waller gun- 
nery trainer, this arrangement appeared to be 
feasible. However, preliminary study indicated 
that with such an arrangement the parallax 


introduced by the separation between the vari- 
ous axes of the testing machine and of the 
gunnery system were almost insurmountable. 
The arrangement finally accepted provides an 
optical target which can be moved in space to 
simulate the desired target motion. In its final 
form, the target can be made to travel any 
desired course whether ideal, such as a pure pur- 
suit course, or real, such as had been actually 
determined by experiments. The final form of 
the optical target system also provides a mov- 
ing picture of an airplane in its correct size and 
attitude. The image of the optical target and its 
position is controlled by a set of cams and 
therefore provides a target course which can 
be accurately and readily reproduced. While 
the work of preparing such a set of cams, which 
is required for each target course, is rather 
extensive, once these cams are prepared only 
a small amount of work is necessary to replace 
them with cams for another course. For each 
particular course the correct gun position is 
known and this is compared with the actual 
gun position obtained in the system under test. 
The gun error is continuously recorded so that 
the actual elevation and azimuth components of 
the gun error are known for each point on the 
course. In the case of certain gunnery equip- 
ment, such as the GE central fire-control sys- 
tem, it is possible to drive the sight mechan- 
ically so as to produce perfect tracking. 

The original machine which was developed 
at the University of Texas has been in opera- 
tion for some time and some of the results ob- 
tained from it have been referred to in previous 
sections of this report. Two additional machines 
were built. One of these is installed at the 
Armament Laboratory at Wright Field and the 
other at the Naval Air Station, Patuxent River, 
Maryland. Results obtained have shown the 
great usefulness of this machine, and without 
question these machines have already saved 
the cost of the original development. The pres- 
ent Texas Testing Machine is described in two 
reports from the University of Texas.^^®’’^^ 
While a large amount of work was done on 
various phases of the development of this 
machine, there are very few reports available 
on this work. Even before the machine was 
finished, alternative methods of carrying out 
some of the operations performed were being 


’ ^NFIDENTIA^ 


PHOTOGRAPHIC METHODS FOR FLIGHT TESTS 


211 


studied and designs prepared. The only other 
available material on this work is a series of 
informal progress reports.^^^'^-^® In the future, 
it should be possible to use the three available 
Texas Testing Machines for most of the assess- 
ment work required on experimental and pre- 
production models of flexible gunnery systems. 
This will provide far more reliable data than 
was previously available and at a considerable 
saving of time and money. 

19.3 photographic methods for 
FLIGHT TESTS 

The first adequate flight tests of flexible gun- 
nery equipment were performed by the Brit- 
ish.^^'^-i^i This test was done by the Gunnery 
Research Unit at Exeter and was an assessment 
of the Mark II gyro gunsight. The first facility 
in the United States for adequately assessing 
flexible gunnery systems by flight test was 
developed by the AAF Proving Ground Com- 
mand at Eglin Field under general guidance 
of Section 7.2. Camera equipment was devel- 
oped and installed in the airplane carrying the 
equipment under test which would record the 
actual relative position of a fighter plane mak- 
ing a simulated attack. A pair of gyros were 
used to determine the roll, pitch and yaw of 
the bomber airplane. Other cameras were used 
for photographing the position of the target 
relative to the line of the gun and the position 
of the target and sight reticle as viewed through 
the sight. After the various films were proc- 
essed the necessary data was read from them 
and the overall error in gun pointing was com- 
puted. Great care was taken to design the ex- 
periment and to control the various conditions 
so that the computed results were statistically 
reliable. 

A large amount of time was required to 
develop the equipment needed by this test and 
to train the necessary personnel. Probably the 
most difficult problem in establishing this 
method was to educate the people concerned in 
the general philosophy of quantitative testing. 
It was found exceedingly difficult to get the 
people running the test to follow the actual 
operation schedule laid out, and to make sure 
that the equipment under test was in proper 
operating condition. Much time was lost due to 


missions being run under improper circum- 
stances. The method of flexible gunnery assess- 
ment developed at Eglin Field has been com- 
pletely described in one of their reports. 

Once a test had been planned, a relatively 
large amount of data could be collected in a 
short time. At first this was not the case be- 
cause of breakdowns of the test equipment and 
the general difficulties of weather and airplane 
failures which are common to all flight tests. 
Even with the delays encountered in taking 
data, the time necessary to analyze the results 
and compute the gun errors was many times 
that necessary to take the original data. Any 
improvement in the method, particularly that 
of analyzing the data, promised large savings 
in time. For this reason an analysis of this 
assessment method was undertaken by the Ap- 
plied Mathematics Group at Northwestern Uni- 
versity.^^2 This analysis was in effect an assess- 
ment of the assessment method being used at 
Eglin Field. It was found that certain approxi- 
mations which had been used to simplify compu- 
tation led to errors which were greater than 
desired. Improved methods of computation were 
recommended and several sets of results were 
computed using them.^^^ As this assessment 
work continued other improvements were de- 
veloped.^^^ Another improvement which was 
developed at Eglin Field was the use of gno- 
monic charts^^^-^^^ for carrying out a large part 
of the computation. 

Before the flexible gunnery assessment 
method had been completely developed at Eglin 
Field, the Navy became interested and re- 
quested NDRC to develop a similar facility at 
the Naval Air Station, Patuxent River, Mary- 
land. As part of this work, the Applied Mathe- 
matics Group at Northwestern University 
undertook a study of existing assessment meth- 
ods, including the one under development at 
Eglin Field. The papers referred to above re- 
port part of that study. An excellent analysis 
of the general photographic method of gunnery 
assesment is given in reference 157. Other re- 
ports were prepared on the problem of de- 
termining the roll, pitch and yaw of the bomber 
airplane by means of gyros and the use of this 
information in correcting the original data for 
this motion. 

In carrying out the request of the Navy, 


212 


SIMULATION AND GUNNERY ASSESSMENT 


Section 7.2 of NDRC contracted with the North- 
western Technological Institute to do the work 
necessary to provide the Navy with the flexible 
gunnery testing facility it desired. Northwest- 
ern, after reviewing the Eglin Field method of 
analysis, decided that the analysis work could 
be done with less effort by means of special 
mechanisms. A set of such mechanisms was 
developed and built and put into use for the 
Navy. Duplicates were subsequently built for 
Eglin Field. The most complete description of 
the theory and operation of this photographic 
method of flexible gunnery assessment is given 
in a rather extensive set of reports prepared 
by Northwestern. These reports^®^ should be 
required reading for anyone undertaking to 
understand this method and its use. North- 
western also undertook to prepare a computer’s 
manual for processing the aerial gunnery as- 
sessment film obtained by this method. This 
manual is not yet complete but the first two 
parts have been finished. The first part is in- 
cluded in the report previously mentioned^®^ 
and the second part is given in a separate re- 
port.i®^ One useful computing device which was 
suggested for use in carrying out some of the 
work of analyzing the assessment films was 
suggested by the Applied Mathematics Group 
at Columbia University. This is known as the 
stereographic spherimeter, and is described in 
two reports prepared by them.^^^’^®® 

In the flexible gunnery assessment work done 
both at Eglin Field and Patuxent River, it was 
always assumed that the bomber carrying the 
equipment under test was flying a straight-line 
course at constant speed. Under any other con- 
ditions errors would be introduced into the 
result. Since it was desirable to carry on some 
tests with the bomber taking evasive action, 
some work was done to modify the method so 
as to adapt it to this situation. This is described 
in reference 167. 

The original evaluation test of the B-29 
central fire-control system, which was carried 
out by Eglin Field, was done before the photo- 
graphic method of assessment had been devel- 
oped. After the development of this assessment 
method, the AAF planned to re-evaluate the 
B-29’s using it. However, the General Electric 
Company decided that it would be to their ad- 
vantage to have a testing facility of their own 


which could be used in the improvement of the 
present B-29 system and the development of 
new systems. They developed such a facility at 
Brownsville, Texas and succeeded in getting a 
fair amount of data by the end of the war. This 
method used a somewhat different technique 
than that in use at either Eglin Field or 
Patuxent River. It was one which was par- 
ticularly adaptable to remote control turrets 
using electric servos. No adequate report of the 
details of the method is available but the 
program for the first set of extensive tests is 
described. 

4 OTHER METHODS 

Two other methods of flexible gunnery as- 
sessment were proposed. The first of these^®*'^ 
made use of distant reference points. This 
method was applied by the University of New 
Mexico in a few tests which they performed on 
the B-29. It was never fully analyzed and there- 
fore its errors are not known. However, it is 
considerably simpler than any of the methods 
just discussed and should not be overlooked in 
future work. The other method^^^ is essentially 
a vector method. It is also considerably simpler 
than the Eglin Field or Patuxent River meth- 
ods. A preliminary study of this method^”^^ in- 
dicates that its accuracy is comparable. 

One interesting training device which was 
developed during the war is the frangible bul- 
let. This is a .30-caliber bullet which breaks up 
on striking very light armor. It can be fired at 
pursuit airplanes while they are making sim- 
ulated attacks on the bomber. By modifying 
standard computing systems for the ballistics 
of this bullet, it is possible to give a gunner 
training under very realistic conditions. In the 
system finally developed, special armored P-63’s 
were used to make the simulated attacks and 
these contained a hit indicator which counted 
the hits and flashed a light when a hit was 
being made. This system provided one psycho- 
logical condition which is missing in all fhe 
assessment methods, namely the ability to fire 
live ammunition at the target in flight. For this 
reason, it was suggested that frangible bullets 
be used as an assessment means. However, this 
has two serious objections which were not fully 
understood by those suggesting its use. The first 


' [confidentlaT 


DISPERSION AND THE FIGURE OF MERIT 


213 


is that it is not possible to accurately transpose 
the results obtained with frangible bullets into 
results which would have been obtained with 
standard live ammunition. The second is that 
a record of the number of hits on the target, 
which was a rather small percentage of the 
total rounds fired, is very inadequate evidence 
of the performance of the system. This is dis- 
cussed in reference 172. 

Although this report is concerned with flex- 
ible gunnery systems, some mention should be 
made of methods for assessing fighter gunnery. 
Considerable work on this was done by the 
Applied Mathematics Group at Northwestern, 
and their results are given in six reports.^'^^-^^® 

5 DISPERSION AND THE EIGURE OF 
MERIT 

The usual results obtained by any test of a 
flexible gun system are given as the error in the 
gun position. These error data in their simple 
form are not particularly useful. This is because 
the effect of such an error on the ability of the 
system to bring down an attacking fighter is 
not at all evident. In fact the given angular 
error in gun position is much more serious at 
longer ranges than at shorter ranges. In addition, 
its effect is controlled to a large extent by the 
dispersion pattern of the bullets. A number of 
tests were run to determine the actual dis- 
persion pattern of various flexible gunnery sys- 
tems. By far the most outstanding of these 
tests were run by the Flexible Gunnery School 


at Laredo, Texas and the results of such tests 
on the B-17, B-24 and B-29 are given in two 
of their reports. A detailed description 
of the testing method has also been prepared by 

them.^^2 

The final measure of effectiveness of ac- 
curacy of a gunnery system should be expressed 
in terms of expected damage at the target. Con- 
siderable effort was expended in finding a suit- 
able figure of merit of this sort and in develop- 
ing methods for computing it. The general 
philosophy of such a figure of merit is dis- 
cussed in reference 179. The figure of merit 
which was finally adopted for use in all the 
flexible gunnery assessment programs was the 
probability of a hit when a single bullet is fired. 
The details of this figure of merit and methods 
of computing it from gun error data will be 
found in a group of four reports. A 
very complete and detailed analysis of this 
problem was made in England.^®^ 

A much more realistic method of evaluating 
the effectiveness of aerial gunnery is based on 
the idea of a duel between a fighter and a 
bomber. In this case an attempt is made to 
determine which airplane would be shot down 
first or which side would be successful in a 
duel between groups of fighters and bombers. 
The problem of answering such questions by 
evaluating the probability of either plane shoot- 
ing down the other, while much more realistic, 
is considerably more difficult. A fair amount of 
work on this has already been accomplished, 
principally in England,^®®’^®®’^^^*^^^ but consider- 
ably more needs to be done. 




lONFIDENTIAL 


7 


Chapter 20 


DISCUSSION ON FUTURE WORK 


20.1 INTRODUCTION 

F uture development work in airborne fire- 
control systems should be of two types. The 
first of these is the continual improvement of 
systems now in existence or under development. 
The main objective of such work will be to 
obtain the best performance from the systems 
that can be put into use in the immediate fu- 
ture. If another national emergency arises soon, 
this is the only type of equipment that will be 
available for use. It is unlikely that such work 
will lead to any startling improvements in per- 
formance over that of present systems. The 
second type of development work is relatively 
long term in nature and would involve a search 
for systems which may be quite different than 
those in existence at present. The greatest pos- 
sibility of making large improvements in per- 
formance is provided by such long-term work. 
However, such work must be based on estimates 
of the character of future aerial warfare and 
would have very little effect on equipment 
which would have to be used in the next few 
years. One major problem which must be solved 
is that of deciding what proportion of the total 
available effort is to be put on these two types 
of work. It goes without saying that neither 
one can be neglected. In this discussion only 
that work pertaining to the immediate future 
will be considered. 

20 2 TRACKING CONTROLS 

Evidence is already available that very 
worth-while improvements in the accuracy of 
gunnery systems can be obtained by improved 
methods of locating target position. One way 
in which this can be accomplished in the case of 
manual tracking is by the use of aided tracking 
controls. It is very probable that this should be 
made a part of all new tracking-control systems. 
While it was difficult to modify turrets produced 
during the war so that they would have aided 
tracking control, very little effort is required 
to provide it in new turret designs. Another 


very important aid to the gunner is line of sight 
stabilization. This has already been given con- 
siderable consideration and has been shown to 
contribute a substantial increase in accuracy 
in the performance of the system. Here also 
the probable type of future fire-control systems 
makes it possible to include stabilization in 
future designs with the expenditure of very 
little additional effort. 

With present fire-control systems, by far the 
largest source of error has been the poor qual- 
ity of the ranging. This means that one of the 
best ways of improving the accuracy of future 
systems is to improve the accuracy of ranging. 
The ranging controls used in manually operated 
systems during World War II were relatively 
crude. In addition, the necessity of doing rang- 
ing simultaneously with tracking made it very 
difficult to do either satisfactorily. Perhaps the 
best way of obtaining better range data is by 
the use of radar. This cannot be accomplished 
satisfactorily until present radar range sets 
are improved to the point where they can be 
easily installed and are less susceptible to the 
effects of multiple targets. 

The use of completely automatic radar for 
tracking and ranging offers considerable 
promise. However, the cost, weight, and com- 
plexity of such equipment may make it un- 
profitable to rely on it completely. There is no 
doubt that for fighting at night or in bad 
weather, radar offers the only possible method. 
In any event, the use of both radar and manual 
operation should be the subject of further study. 
One of the major problems still unsolved is 
that of determining how these two tracking 
and ranging methods can best be exploited. 

20-3 COMPUTERS 

A wide variety of gunnery computers of both 
the local and remote-control types was de- 
veloped during World War II. It was found 
relatively easy to design these computers so 
that they would determine the required ballistic 


214 


feONFIDENTIALT] 


ASSESSMENT 


215 


lead accurately. In fact, in most cases the ac- 
curacy of the ballistic lead provided was con- 
siderably greater than was warranted in view 
of inaccuracies present in other parts of the 
system. The main requirement which should be 
met by future ballistic computers is that they 
should be so designed as to make it possible to 
adapt them to various types of ammunition. 
This has already been accomplished to a large 
extent in some designs. The other requirement 
is that the ballistic computers should be simpli- 
fied as much as possible so that the performance 
provided by them is in a better balance with 
that of the other parts of the system. 

The largest errors present in existing com- 
puters occur in the computation of kinematic 
lead. Present computers are sensitive to the 
type of target course largely because the only 
course data used as inputs are present angle 
and range. The effects of range rate and an- 
gular acceleration are taken into account only 
through a calibration procedure which adapts 
the computer to a particular course. The next 
major step to be made in the improvement of 
kinematic-lead computers is to provide them 
with range rate and angular rate data and 
design them to use this additional information. 
This has been impossible in the past largely 
because the accuracy of such data as were 
available was inacceptable. The use of im- 
proved tracking and ranging methods will make 
it possible to provide range rate and angular 
rate data which can be used by improved kine- 
matic-lead computers. In addition, all future 
computers should be based on the use of gyros. 
This calls for some improvement in the gyros 
themselves. Considerable work has already 
been done in this direction by Sperry, General 
Electric, Fairchild, and Westinghouse, and this 
work should be evaluated and made the basis 
for the future development of aerial gunnery 
equipment. 

20 ^ PSYCHOLOGICAL DESIGN 

The psychological problems arising in aerial 
gunnery systems have been given far too little 
consideration in the past. The evidence that 
such problems existed first arose in the train- 
ing field and a large amount of effort was put 
into solving them. One general problem which 


has not been fully appreciated has been the 
necessity of designing the controls of equip- 
ment so that they can be operated by a man in 
the best way. One of the biggest opportunities 
for improvement in performance lies in this 
field. It is also very important that people con- 
cerned with training be given an opportunity 
to evaluate new equipment, while still in the 
development stages, from the viewpoint of 
training. This will not only assist the training 
people in developing an adequate training pro- 
gram but will often prevent equipment from 
getting into the field which is difficult to op- 
erate. As an aid to these problems, it is desir- 
able to learn more about the performance of a 
human being as a component in a tracking and 
ranging control system. 

20-5 ASSESSMENT 

The tremendous advantage of using a testing 
machine such as the Texas Tester over the 
usual flight test has already been demonstrated. 
This does not mean that the necessity for flight 
test has been eliminated but it does mean that 
most of the testing of experimental equipment 
and preproduction models can be accomplished 
on such a machine. This also makes it possible 
to carry out tests at a very early stage in de- 
velopment. It also makes it possible to select 
the most promising equipment from a number 
of competing developments, and thereby con- 
centrate the effort and save considerable time 
and money. 

This same sort of result can also be obtained 
by early mathematical analysis of various pro- 
posed systems. Such an analysis may often pro- 
vide very valuable evaluation on such systems 
while they are in a very early stage of develop- 
ment. It also offers a very useful tool in plan- 
ning the development program. During World 
War II most of the mathematical analysis of this 
sort was on equipment either in production or 
in a very late stage of development. In the 
future, such analysis should be one of the first 
things done when a new system is proposed. 

There is ample room for improvement in the 
various existing methods of gunnery assess- 
ment. The present Texas Testing Machine is 
only the first model of such a machine. The 
needs for it were so pressing that every effort 


! 


JONFIDENTIAL 


216 


DISCUSSION ON FUTURE WORK 


was made to complete three of these as soon as 
possible rather than to provide a machine of 
improved performance at a much later date. 
The usefulness of this machine is so great that 
it will be well worth while to put some effort 
into producing a model which is more flexible 
than the present one and which will handle a 
much wider variety of equipment and target 
courses. The present photographic method of 
flight testing has reached a high state of per- 
fection and it is doubtful if any large effort 
should be put into its improvement. However, 
the distance reference point method and the 
vector or own-speed method offer great promise. 
It is conceivable that either or both of these 
might provide a method with accuracy equal to 
that of the present method, but requiring far 
less work in analyzing the results. The develop- 
ment of both of these methods should be carried 
forward to the point where they can be com- 
pared with the present methods. In addition, 
some facility should be developed which can be 
used for carrying out tactical studies on the use 
of aerial gunnery equipment. This facility 
should be capable of providing all the control 
conditions and quantitative data that are re- 
quired by any good experimental work. 

206 WEAPONS 

The standard weapon used in airplanes for 
bomber defense during World War II was the 
.50-caliber machine gun. Its performance is ex- 
cellent and also considerably better than any of 
the small caliber weapons which were previously 
developed and used. However, this weapon was 
never used at its full effectiveness because of 
the inaccuracies of the fire-control system of 
which it was a part. No one questions the de- 
sirability of developing a weapon of larger 
caliber and greater range and higher-firing 
rate. The probable extent of improvements in 
this direction, however, does not offer as much 


overall improvement in the performance of 
gunnery systems as improvements in computer 
performance. Developments in new weapons 
should certainly continue, but they should not 
be made at the expense of developments which 
will lead to increased accuracy in other parts 
of the gunnery system. The most profitable di- 
rection for weapon development is in the direc- 
tion of large caliber projectiles. One such 
projectile is the spin-stabilized rocket. While 
this probably is a relatively long-term develop- 
ment, it is possible that a suitable projectile of 
this sort would become available in the next 
few years. 

20 7 PLANNING AND CONTROL 

Perhaps the most serious lack in the fire 
control development work which was done dur- 
ing World War II was the lack of an adequate 
planning and control group within the Army 
Air Force. Most of the initiative for these de- 
velopments came from industry. The Army Air 
Force exerted very little direction over this 
work and appeared to have no coordinated plan. 
As a result, a lot of competing developments 
were carried on simultaneously and the choice 
of the final system was not made on any logical 
basis. To avoid this difficulty in the future, it is 
necessary for the Army Air Forces to have a 
central planning group which has the authority 
to control the overall development program. It 
is also necessary to provide much greater use 
of highly trained and experienced civilians. In 
the past the direction of important develop- 
ment work has been given to officers or civilians 
who had neither the background nor the ability 
to do it properly. This situation has been 
further aggravated by the fact that the same 
organization has been responsible for procure- 
ment and production as well as research and 
development. There is ample experience in in- 
dustry to show that these two types of functions 
should be separate. 


XJTTPIDENTIAL 


APPENDIX 


Remark 


INDEX OF DIFFERENTIAL ANALYZER SOLUTIONS FOR GUIDED BOMB 
TRAJECTORIES (AZON AND RAZON) 


T he present index does not attempt to explain 
guided bombing or even to give an account of 
the use of the differential analyzer in the study 
to date of the guiding problem. It is merely a 
ready-reference record from which the various 
trajectory solutions may be conveniently se- 
lected. In the foreword which follows, the equa- 
tions solved by the analyzer are given together 
with some of the more pertinent physical param- 
eters, initial and final conditions, and so on. 
There is also included a brief explanation of the 
tabular form of the index itself. 


where and are the elevator and rudder de- 
flections measured in degrees from the position 
of zero control, A is the area of cross section of 
the bomb, p is the air density at altitude z, and 
Coy Cs, Cl are ballistic coefficients of the bomb, 
given as empirical functions of 8e and Sr- M is 
the mass of the bomb. 

All trajectories listed under RDA No. 119 are 
for range-only control. In this case equations (1) 
were used, where 8^ and Sr are zero. In the case 
of rudder control the following approximate 
equations were used: 


Foreword 

If it is assumed that the lift force acting on a 
bomb as a result of elevator control remains 
parallel to the original vertical plane of projec- 
tion when rudder control is applied, then the 
differential equations for the bomb trajectory 
are 


X = — xj/ x^ A- 


y = ^x'^A-y^A-z^ 


d{bE,^R)Z) -f- 


s(8R,z)y 

^ x^ A- z^_ 


I (8e,z) z 


x"^ -f ^2 


/ 


A-y^A- z"^) 


1^— d {bEARy^) 2/ + s {bR,z) 

z = —z ^^x’^ A- y‘^ A- z^^{bE, 

I {bEyZ) x 




( 1 ) 


bR,z) -f- 


/• 


s {bR,z) y ] 

A- z^j 


+ • 


{x^ A- y^ A- Z^) —y 


+ ? 

where Xy y, z are Cartesian coordinates in a sys- 
tem whose origin is stationary in the air mass 
and at ground level directly beneath the point 
of release of the bomb, and whose x axis is in 
the direction of the velocity of the airplane with 
respect to the air at release. The functions 
d{bEybR,z)y s{hRyZ), l{hEyZ) are defined by 


d (bEybRyZ) = (dEybR), 

HSr,z) = ^^CsiSn), 


( 2 ) 


liSE,z) =^^Cl(Se), 


x = — 


x(di8EybR,z) A- ^ i^RyZ)^ 


/.r2 -I- ^2^ 

y = [—d {bE,bRyZ)y -f s{bR,z) -f zA / x^ A- z^, 


z ^(bEybRy. 


^ , S (^RyZ) y ^ , ,, 

2 ) + —/=== - I {^EyZ)X 


4/^2 ; 


(3) 
— 2 /* 


These were obtained by replacing ^ 2 _|_^ 2_|_^2 
the drag and side-force terms by ^ x^-\-y'^-\-z^ 
‘^y and in the lift-force term by x^A-'^"^- All 
runs labeled RDA 120 are for equations (3). 
These equations reduce to equations (1) when 
s and y are zero. In RDA No. 121 equations (1) 
were used, with range-only control. In these runs 
the functions Cb and Cl were plotted against 8^ 
on input tables and fed in continuously during 
the course of the solution whenever control was 
applied. For all other runs the full value of Cp, 
Cs or Cl for any specified elevator or rudder 
position was set in at the indicated times. 

Except where otherwise noted the function 
used for density was 


= 0.959 

Po 

where p^ = 0.002378 slug/ft^ is air density at sea 
level. 

In RDA No. 119, Edition 1, and RDA No. 120, 
Edition 2, the value used for A was 1.865 ft^, and 
for M 1,000 lb. In all other editions except where 


lONFIDENTIAL 


9 


217 


218 


APPENDIX 


noted the values used for both Azon and Razon 
were in the case of the 1,000-lb bomb A = 1.89 
ft^ M = 1,020 lb, and for the 2,000-lb bomb 
A = 2.89 ftS M = 2,160 lb. 

The sources of the various values of Cd, Cs, Cl 
used are given for each edition. For Editions 8 
and 9 the coefficients were obtained by varying 
the Wyckoff coefficients by ±20 per cent. These 
runs are to be used to obtain, by interpolation 
or extrapolation, data for bombs with different 
ballistic coefficients. Also included in Edition 8 
are some runs, Nos. 123-129, using coefficients 
corresponding to half or three-quarters control 
for an early Razon bomb with long horizontal 
fins or ''sideburns.’’ 

The initial velocity of the bomb, Vq, is in the 
horizontal direction and given in miles per hour, 
except where otherwise specified. The time of 
flight, tf, is given in seconds. Rudder and elevator 
deflection hu and are in degrees. The range 
and sidewise deflection at impact, x{tf)y 
are given in feet. The column headed gives the 
time of application of the control indicated on 
that same line. Where there is a blank, no control 
was applied and the trajectory is free fall. When 
for any run the first value of listed is not zero, 
then no control has been applied up to that 
instant. This control is understood to continue 
until a new value of with different control is 
listed, or until impact if no change in control is 
indicated. 

RDA No. 119 Edition No. 1. Initial Altitude 15,000 feet. 

1,000-pound Razon (Octagonal Shroud) Range-Only 
Control 


(Akron Coefficients, 10-27-43) 


Run 

No. 

Vo 

5 b 

Cd 

Cl 


tf 

X{tf) 


100 

0° 

0.406 

0 


32.294 

4218 

116 

100 

20° 

0.692 

0.981 

0 

36.284 

8505 

131 

100 

—20° 

0.692 

—0.981 

0 

33.301 

195 

113 

100 

20° 

0.692 

0.981 

8 

35.852 

8282 

130 

100 

—20° 

0.692 

—0.981 

8 

33.408 

503 

112 

100 

20° 

0.692 

0.981 

15.5 

34.852 

7280 

129 

100 

—20° 

0.692 

—0.981 

15.5 

33.186 

1447 

111 

100 

20° 

0.692 

0.981 

23 

33.249 

5597 

128 

100 

—20° 

0.692 

—0.981 

23 

32.678 

2945 

110 

100 

20° 

0.692 

0.981 

27 

32.619 

4750 

127 

100 

—20° 

0.692 

—0.981 

27 

32.428 

3712 


RDA No. 119 Edition No. 1 {Continued) 

Run 


No. 

Vo 

Se 

Cd 

Cl 


tf 

X(tf) 


175 

0° 

0.406 

0 


32.524 

7285 

115 

175 

20° 

0.692 

0.981 

0 

38.342 

12306 

122 

175 

—20° 

0.692 

—0.981 

0 

32.430 

2754 

109 

175 

20° 

0.692 

0.981 

8 

37.426 

11986 

126 

175 

—20° 

0.692 

—0.981 

8 

32.832 

3285 

108 

175 

20° 

0.692 

0.981 

15.5 

35.747 

10762 

125 

175 

—20° 

0.692 

—0.981 

15.5 

32.882 

4381 

107 

175 

20° 

0.692 

0.981 

23 

33.680 

8822 

124 

175 

—20° 

0.692 

—0.981 

23 

32.644 

5952 

106 

175 

20° 

0.692 

0.981 

27 

32.849 

7877 

123 

175 

—20° 

0.692 

—0.981 

27 

32.499 

6745 

101 

250 

0° 

0.406 

0 


32.578 

10245 

71 

250 

20° 

0.692 

0.981 

0 

41.100 

16355 

144 

250 

—20° 

0.692 

—0.981 

0 

31.481 

4965 

105 

250 

20° 

0.692 

0.981 

8 

39.492 

15897 

118 

250 

—20° 

0.692 

—0.981 

8 

32.300 

5804 

104 

250 

20° 

0.692 

0.981 

15.5 

37.013 

14335 

120 

250 

—20° 

0.692 

—0.981 

15.5 

32.636 

7120 

103 

250 

20° 

0.692 

0.981 

23 

35.590 

12442 

119 

250 

—20° 

0.692 

—0.981 

23 

32.651 

8808 

102 

250 

20° 

0.692 

0.981 

27 

33.139 

10917 

117 

250 

—20° 

0.692 

—0.981 

27 

32.606 

9655 

73 

250 

20° 

0.692 

0.981 

8 





0° 

0.406 

0 

27 





—20° 

0.692 

—0.981 

29 

36.865 

12953 

136 

250 

—20° 

0.692 

—0.981 

0 





0° 

0.406 

0 

18 





20° 

0.692 

0.981 

19.3 

32.482 

9121 

137 

225 

—20° 

0.692 

—0.981 

0 





0° 

0.406 

0 

18 





20° 

0.692 

0.981 

19.3 

32.696 

8465 

138 

200 

—20° 

0.692 

—0.981 

0 





0° 

0.406 

0 

18 





20° 

0.692 

0.981 

19.3 

32.897 

7763 

139 

175 

—20° 

0.692 

—0.981 

0 





0° 

0.406 

0 

18 





20° 

0.692 

0.981 

19.3 

33.066 

7017 

140 

225 

—20° 

0.692 

—0.981 

0 





0° 

0.406 

0 

16 





20° 

0.692 

0.981 

17.3 

33.371 

9495 

141 

200 

—20° 

0.692 

—0.981 

0 





0° 

0.406 

0 

16 





20° 

0.692 

0.981 

17.3 

33.502 

8743 

142 

200 

—20° 

0.692 

—0.981 

0 

32.123 

3531 

143 

225 

—20° 

0.692 

—0.981 

0 

31.807 

4267 

148 

250 

20° 

0.692 

0.981 

8 





0° 

0.406 

0 

20 





—20° 

0.692 

—0.981 

22 

35.040 

10157 

149 

250 

20° 

0.692 

0.981 

8 





0° 

0.406 

0 

21 





—20° 

0.692 

—0.981 

23 

35.281 

10568 

150 

250 

20° 

0.692 

0.981 

8 





0° 

0.406 

0 

20.3 





—20° 

0.692 

—0.981 

22.3 

35.107 

10288 



1,000-pound Azon (Square-tail) 
(Akron Coefficients, 10-27-43) 


132 

100 

0° 

0.265 

0 


31.678 

4306 

133 

175 

0° 

0.265 

0 


31.766 

7471 

134 

250 

0° 

0.265 

0 


31.881 

10565 


< ^ONFIDENTIAl| 


APPENDIX 


219 


RDA No. 119 Edition No. 2. Initial Altitude 15,000 feet. 
1,000-pound Azon (Preset elevator control) 


(R. D. Wyckoff Coefficients 12-21-43) 


Run 

No. 

Vo 

5a. 

5b 

Cd 

Cl 


tf 

X{tf) 

23 

250 

0° 

0° 

0.262 

0 


31.855 

10577 

24 

250 

0° 

1° 

0.263 

0.047 

0 

32.06 

10857 

25 

250 

0° 

—1° 

0.263 

—0.047 

0 

31.659 

10293 

26 

250 

0° 

—2° 

0.264 

—0.093 

0 

31.481 

10026 

27 

250 

0° 

2° 

0.264 

0.093 

0 

32.289 

11140 

28 

250 

0° 

3° 

0.270 

0.140 

0 

32.547 

11422 

29 

250 

0° 

—3° 

0.270 

—0.140 

0 

31.332 

9747 

30 

250 

0° 

—4° 

0.276 

—0.178 

0 

31.222 

9522 

31 

250 

0° 

40 

0.276 

0.178 

0 

32.771 

11650 

32 

250 

0° 

5° 

0.286 

0.216 

0 

33.023 

11875 

33 

250 

0° 

—5° 

0.286 

—0.216 

0 

31.139 

9294 


RDA No. 119 Edition No. 2 {Continued) 
2,000-pound Razon 
(R. D. Wyckoff Coefficients 12-21-43) 

Run 

No. 

Vo 

Se 

Co 

Cl 

U 

tf 

X{tf) 

41 

250 

0° 

0.261 

0 


31.489 

10751 

46 

250 

20° 

0.487 

0.739 

0 

35.379 

13969 

42 

250 

20° 

0.487 

0.739 

8 

34.512 

13684 

43 

250 

20° 

0.487 

0.739 

15.5 

33.384 

12832 

44 

250 

20° 

0.487 

0.739 

23 

32.171 

11607 

47 

250 

20° 

0.487 

0.739 

27 

31.687 

11031 

48 

250 

—20° 

0.487 

—0.739 

8 

31.045 

8078 

49 

250 

—20° 

0.487 

—0.739 

15.5 

31.336 

8912 

50 

250 

—20° 

0.487 

—0.739 

23 

31.463 

9974 

51 

250 

—20° 

0.487 

—0.739 

27 

31.483 

10477 

52 

175 

0° 

0.261 

0 


31.405 

7577 

63 

175 

20° 

0.487 

0.739 

0 

34.070 

10192 

55 

175 

20° 

0.487 

0.739 

8 

33.594 

10010 

54 

175 

20° 

0.487 

0.739 

15.5 

32.837 

9361 

62 

175 

20° 

0.487 

0.739 

23 

31.936 

8332 

57 

175 

20° 

0.487 

0.739 

27 

31.565 

7820 

58 

175 

—20° 

0.487 

—0.739 

8 

31.383 

5270 

59 

175 

—20° 

0.487 

—0.739 

15.5 

31.487 

5930 

60 

175 

—20° 

0.487 

—0.739 

23 

31.463 

6872 

61 

175 

—20° 

0.487 

—0.739 

27 

31.424 

7334 


RDA No. 120 Edition No. 2. Initial Altitude 15,000 feet. 
1,000-pound Razon (Octagonal Shroud) 

(Akron Coefficients, 10-27-43) 


Run 


No. 

^0 

8r 

Se 



Cb 

h 

Xitf) 

H(tf) 

83 

100 

00 

00 

0.406 

0 

0 

32.286 

4218 

0 

4 

100 

20° 

00 

0.692 

0.981 

0 

8 34.386 

4052 

3758 

2 

100 

200 

00 

0.692 

0.981 

0 

15.5 33.814 

4139 

2797 

5 

100 

20° 

00 

0.692 

0.981 

0 

23 32.930 

4201 

1297 

6 

100 

200 

00 

0.692 

0.981 

0 

27 32.518 

4215 

513 


175 

00 

00 

0.406 

0 

0 

32.524 

7285 

0 

10 

175 

200 

00 

0.692 

0.981 

0 

8 34.697 

6970 

4174 

9 

175 

200 

00 

0.692 

0.981 

0 

15.5 34.003 

7134 

3016 

8 

175 

200 

00 

0.692 

0.981 

0 

23 33.094 

7254 

1379 

7 

175 

200 

00 

0.692 

0.981 

0 

27 32.664 

7290 

552 


RDA No. 120 Edition No. 2 {Continued) 


Run 

No. 

^0 

5/f 

8e 

Co 




h 

xitf) 

Vitf) 

15 

250 

00 

00 

0.406 

0 

0 


32.591 

10251 

0 

14 

250 

20° 

00 

0.692 

0.981 

0 

8 

35.105 

9749 

4768 

13 

250 

20° 

00 

0.692 

0.981 

0 

15.5 

34.333 

10029 

3325 

12 

250 

200 

00 

0.692 

0.981 

0 

23 

33.308 

10202 

1491 

11 

250 

200 

00 

0.692 

0.981 

0 

27 

32.869 

10237 

535 

87 

250 

200 

200 

0.978 

0.981 

0.981 

8 

41.663 

14246 

5952 

90 

250 

200 

200 

0.978 

0.981 

0.981 

15.5 

38.862 

13537 

4181 

91 

250 

200 

200 

0.978 

0.981 

0.981 

23 

35.062 

11875 

1774 

92 

250 

200 

200 

0.978 

0.981 

0.981 

27 

33.439 

10908 

669 

104 

250 

200 

—200 

0.978 

0.981 

—0.981 

8 

34.695 

5645 

4122 

102 

250 

200 

—200 

0.978 

0.981 

—0.981 

15.5 

34.294 

7057 

2941 

101 

250 

200 

—200 

0.978 

0.981 

—0.981 

23 

33.341 

8803 

1362 

100 

250 

200 

—200 

0.978 

0.981 

—0.981 

27 

32.861 

9651 

564 


RDA No. 120 Edition No. 2 {Continued) 
1,000-pound Azon (Square-tail) 

(Akron Coefficients, 10-27-43) 

c 

6 

tf ^ 

Sr 

Go 

Ga 

U 

tf 

xitf) 

yitf) 

36 

100 

0° 

0.265 

0 


31.685 

4307 

0 

43 

100 

20° 

0.487 

0.513 

8 

32.844 

4204 

I960 

41 

100 

20° 

0.487 

0.513 

15.5 

32.543 

4259 

1469 

42 

100 

20° 

0.487 

0.513 

23 

32.176 

4308 

671 

37 

100 

20° 

0.487 

0.513 

27 

31.812 

4304 

249 

29 

175 

0° 

0.265 

0 


31.770 

7472 

0 

31 

175 

20° 

0.487 

0.604 

8 

33.118 

7260 

2604 

32 

175 

20° 

0.487 

0.604 

15.5 

32.737 

7380 

1868 

35 

175 

20° 

0.487 

0.604 

23 

32.173 

7453 

818 

30 

175 

20° 

0.487 

0.604 

27 

31.910 

7470 

300 

54 

175 

20° 

0.487 

0.513 

15.5 

32.694 

7389 

1584 

20 

250 

0° 

0.265 

0 


31.882 

10563 

0 

27 

250 

20° 

0.487 

0.604 

8 

33.364 

10229 

3010 

23 

250 

20° 

0.487 

0.604 

15.5 

32.923 

10424 

2076 

26 

250 

20° 

0.487 

0.604 

23 

32.312 

10536 

887 

28 

250 

20° 

0.487 

0.604 

27 

32.033 

10560 

323 

55 

250 

20° 

0.487 

0.513 

8 

33.249 

10251 

2539 

49 

250 

20° 

0.487 

0.513 

15.5 

32.850 

10431 

1754 

46 

250 

20° 

0.487 

0.513 

23 

32.293 

10541 

754 

45 

250 

20° 

0.487 

0.513 

27 

32.032 

10563 

277 


RDA No. 120 Edition No. 3. Initial Altitude 15,000 feet, 
1,000-pound Azon 

(R. D. Wyckoff Coefficients, 12-21-43) 

Run 

No. 


Sr 

Co 

c. 


C 

xitf) 

vitf) 

1 

250 

00 

0.262 

0 


31.853 

10573 

0 

9 

250 

20° 

0.580 

0.637 

0 

34.050 

9755 

3841 

5 

250 

200 

0.580 

0.637 

5 

33.932 

9994 

3396 

7 

250 

20° 

0.580 

0.637 

10 

33.684 

10194 

2884 

34 

250 

200 

0.580 

0.637 

15 

33.288 

10363 

2229 

35 

250 

200 

0.580 

0.637 

20 

32.765 

10486 

1427 

36 

250 

200 

0.580 

0.637 

25 

32.232 

10554 

613 

15 

250 

200 

0.580 

0.637 

2.5 






00 

0.262 

0 

7.5 

31.966 

10417 

522 

14 

250 

200 

0.580 

0.637 

7.5 






00 

0.262 

0 

12.5 

32.083 

10452 

623 

22 

250 

200 

0.580 

0.637 

12.5 






00 

0.262 

0 

17.5 

32.199 

10444 

751 




;ONFIDENTIAL 


220 


APPENDIX 


RDA No. 120 Edition No. 3 {Continued) 


Run 

No. 

^0 

8 r 

Co 

Cs 

*1 


X ( tf ) 

y ( tf ) 

17 

250 

200 

0.580 

0.637 

17.5 






0° 

0.262 

0 

22.5 

32.283 

10487 

819 

18 

250 

20° 

0.580 

0.637 

22.5 






OO 

0.262 

0 

27.5 

32.262 

10535 

712 

20 

250 

200 

0.580 

0.637 

27.5 

32.017 

10568 

278 

23 

250 

200 

0.580 

0.637 

5 






—200 

0.580 

—0.637 

10 






200 

0.580 

0.637 

15 






—200 

0.580 

—0.637 

20 






200 

0.580 

0.637 

25 






—200 

0.580 

—0.637 

30 

33.399 

10083 

312 


RDA No. 120 Edition No. 4. Initial Altitude 15,000 feet. 





2,000-pound Razon 






(R. 

D. Wyckoff Coefficients 

, 12-21-43) 


Run 











No. 

^0 

Sb 

do 

Co 

c. 



if 

Xitf ) 

y ( tf ) 

138 

175 

0° 

00 

0.261 

0 

0 

0 

31.404 

7576 

0 

100 

175 

OO 

20 

0.265 

0 

0.155 

0 

31.796 

8152 

0 

101 

175 

0° 

— 20 

0.265 

0 

—0.155 

0 

31.140 

7028 

0 

102 

175 

0° 

— 50 

0.289 

0 

—0.303 

0 

30.987 

6505 

0 

103 

175 

OO 

50 

0.289 

0 

0.303 

0 

32.150 

8671 

0 

104 

175 

OO 

70 

0.312 

0 

0.384 

0 

32.443 

8963 

0 

105 

175 

OO 

— 70 

0.312 

0 

—0.384 

0 

30.992 

6226 

0 

106 

175 

OO 

—100 

0.325 

0 

—0.485 

0 

30.951 

5854 

0 

107 

175 

OO 

100 

0.325 

0 

0.485 

0 

32.856 

9318 

0 

108 

175 

20 

00 

0.265 

0.155 

0 

0 

31.429 

7570 

584 

109 

175 

50 

00 

0.289 

0.303 

0 

0 

31.556 

7542 

1130 

112 

175 

70 

00 

0.312 

0.384 

0 

0 

31.688 

7519 

1437 

111 

175 

100 

OO 

0.352 

0.485 

0 

0 

31.855 

7466 

1801 

92 

175 

20 

20 

0.269 

0.155 

0.155 

0 

31.760 

8129 

595 

93 

175 

— 20 

— 20 

0.269 

—0.155 

—0.155 

0 

31.168 

7024 

— 579 

94 

175 

— 50 

— 50 

0.307 

—0.303 

—0.303 

0 

31.105 

6484 

—1094 

95 

175 

50 

50 

0.307 

0.303 

0.303 

0 

32.292 

8642 

1189 

96 

175 

70 

70 

0.363 

0.384 

0.384 

0 

32.700 

8878 

1516 

97 

175 

— 70 

— 70 

0.363 

—0.384 

—0.384 

0 

31.230 

6171 

—1370 

98 

175 

—100 

—100 

0.443 

—0.485 

—0.485 

0 

31.398 

5772 

—1701 

99 

175 

100 

100 

0.443 

0.485 

0.485 

0 

33.266 

9106 

1916 

137 

175 

200 

OO 

0.487 

0.739 

0 

8 

32.410 

7422 

2330 

136 

175 

200 

OO 

0.487 

0.739 

0 

15.5 

32.120 

7510 

1662 

135 

175 

20° 

0° 

0.487 

0.739 

0 

23 

31.698 

7545 

709 

134 

175 

200 

OO 

0.487 

0.739 

0 

27 

31.496 

7574 

240 

(See RDA No. 119, Ed. No. 2 for dR = 

0 °, 8 e 

= ± 20°) 

81 

175 

—200 

—200 

0.713 

—0.739 

—0.739 

8 

32.357 

5181 

—2157 

82 

175 

200 

200 

0.713 

0.739 

0.739 

8 

34.627 

9725 

2568 

83 

175 

200 

200 

0.713 

0.739 

0.739 

15.5 

33.622 

9236 

1820 

84 

175 

-20° 

-20° 

0.713 

—0.739 

—0.739 

15.5 

32.183 

5893 

—1557 

85 

175 

—200 

—200 

0.713 

—0.739 

—0.739 

23 

31.744 

6863 

— 701 

86 

175 

200 

200 

0.713 

0.739 

0.739 

23 

32.243 

8309 

777 

79 

175 

200 

200 

0.713 

0.739 

0.739 

27 

31.661 

7826 

247 

80 

175 

—200 

—200 

0.713 

—0.739 

—0.739 

27 

31.512 

7332 

— 231 

49 

250 

00 

00 

0.261 

0 

0 


31.488 

10745 

0 

39 

250 

00 

20 

0.265 

0 

0.155 

0 

32.017 

11444 

0 

40 

250 

00 

— 20 

0.265 

0 

—0.155 

0 

31.042 

10072 

0 

41 

250 

00 

60 

0.289 

0 

0.303 

0 

32.680 

12119 

0 

42 

250 

00 

— 50 

0.289 

0 

—0.303 

0 

30.737 

9426 

0 

43 

250 

00 

70 

0.312 

0 

0.384 

0 

33.068 

12468 

0 

45 

250 

OO 

— 70 

0.312 

0 

—0.384 

0 

30.624 

9072 

0 

46 

250 

00 

100 

0.352 

0 

0.485 

0 

33.652 

12908 

0 

48 

250 

00 

—100 

0.352 

0 

—0.485 

0 

30.565 

8637 

0 

36 

250 

20 

00 

0.265 

0.155 

0 

0 

31.521 

10734 

735 

37 

250 

50 

00 

0.289 

0.303 

0 

0 

31.666 

10682 

1431 

34 

250 

70 

00 

0.312 

0.384 

0 

0 

31,793 

10631 

1806 

35 

250 

100 

00 

0.352 

0.485 

0 

0 

32.009 

10550 

2270 


RDA No. 120 Edition No. 4 {Continued) 


Run 

No. 

^0 

8r 

8e 

Co 


Cl 

h 

tf 

X itf) 

y(tf) 

50 

250 

20 

20 

0.269 

0.155 

0.155 

0 

32.056 

11431 

757 

51 

250 

20 

— 20 

0.269 

0.155 

—0.155 

0 

31.075 

10058 

708 

53 

250 

50 

50 

0.307 

0.303 

0.303 

0 

32.801 

12050 

1524 

54 

250 

50 

— 50 

0.307 

0.303 

—0.303 

0 

30.875 

9388 

1346 

55 

250 

70 

70 

0.363 

0.384 

0.384 

0 

33.402 

12329 

1955 

56 

250 

70 

— 70 

0.363 

0.384 

—0.384 

0 

30.924 

8985 

1669 

57 

250 

10° 

100 

0.443 

0.485 

0.485 

0 

34.220 

12643 

2449 

59 

250 

10° 

—100 

0.443 

0.485 

—0.485 

0 

31.072 

8494 

2057 

12 

250 

200 

00 

0.487 

0.739 

0 

0 

32.751 

10274 

3394 

133 

250 

20° 

00 

0.487 

0.739 

0 

8 

32.584 

10490 

2715 

132 

250 

20° 

00 

0.487 

0.739 

0 

15.5 

32.257 

10643 

1852 

131 

250 

200 

00 

0.487 

0.739 

0 

23 

31.789 

10727 

770 

130 

250 

200 

00 

0.487 

0.739 

0 

27 

31.588 

10743 

265 

(See RDA 

No. 119, Ed. No. 2 for bR = 0 °, 8e ■ 

= ± 20 °) 

52 

250 

200 

200 

0.713 

0.739 

0.739 

0 

36.571 

13178 

3836 

68 

250 

—200 

—200 

0.713 

—0.739 

—0.739 

8 

32.118 

7934 

—2407 

69 

250 

200 

200 

0.713 

0.739 

0.739 

8 

35.644 

13196 

3116 

66 

250 

200 

200 

0.713 

0.739 

0.739 

15.5 

34.219 

12626 

2100 

67 

250 

—200 

—200 

0.713 

—0.739 

—0.739 

15.5 

32.064 

8850 

—1676 

64 

250 

—200 

—200 

0.713 

—0.739 

—0.739 

23 

31.754 

9959 

— 720 

65 

250 

200 

200 

0.713 

0.739 

0.739 

23 

32.504 

11574 

842 

62 

250 

200 

200 

0.713 

0.739 

0.739 

27 

31.798 

11030 

273 

63 

250 

—200 

—200 

0.713 

—0.739 

—0.739 

27 

31.589 

10479 

— 253 

10 

250 

200 

00 

0.487 

0.739 

0 

5 






00 

0° 

0.261 

0 

0 

18 






—200 

00 

0.487 

—0.739 

0 

20 

32.275 

10474 

254 

11 

250 

00 

200 

0.487 

0 

0.739 

0 

35.379 

13969 

0 

12 

250 

200 

00 

0.487 

0.739 

0 

0 

32.751 

10274 

3394 

14- 











15 

250 

20° 

00 

0.487 

0.739 

0 

5 






00 

00 

0.261 

0 

0 

18 






—200 

50 

0.515 

—0.739 

0.303 

20 






—200 

—100 

0.578 

—0.739 

—0.485 

30 

32.555 

10914 

221 

16 

250 

200 

00 

0.487 

0.739 

0 

5 






00 

00 

0.261 

0 

0 

15 






—100 

00 

0.352 

—0.485 

0 

17 

31.928 

10525 

9 

17 

250 

200 

00 

0.487 

0.739 

0 

5 






00 

00 

0.261 

0 

0 

15 






—100 

00 

0.352 

—0.485 

0 

17 

31.952 

10533 

— 12 

19 

250 

200 

OO 

0.487 

0.739 

0 

5 






00 

00 

0.261 

0 

0 

15 






—100 

00 

0.352 

—0.485 

0 

17 

31.947 

10530 

26 

21 











23 

250 

200 

00 

0.487 

0.739 

0 

0 






70 

00 

0.312 

0.384 

0 

8.5 






— 70 

00 

0.312 

—0.384 

0 

15 

31.757 

10491 

149 

24 

250 

200 

00 

0.487 

0.739 

0 

0 






70 

00 

0.312 

0.384 

0 

8.5 






— 70 

OO 

0.312 

—0.384 

0 

14 

31.760 

10496 

15 

25 

250 

200 

200 

0.713 

0.739 

0.739 

0 






70 

70 

0.363 

0.384 

0.384 

8.5 






— 70 

70 

0.363 

—0.384 

0.384 

14 

33.705 

12235 

— 131 

26 

250 

200 

200 

0.713 

0.739 

0.739 

0 






70 

00 

0.312 

0.384 

0 

8.5 






— 70 

00 

0.312 

—0.384 

0 

15 

32.554 

10768 

72 

27 

250 

200 

200 

0.713 

0.739 

0.739 

0 






70 

00 

0.312 

0.384 

0 

8.5 






— 70 

00 

0.312 

—0.384 

0 

14 

32.316 

10702 

— 29 

28 

250 

200 

200 

0.713 

0.739 

0.739 

0 






70 

00 

0.312 

0.384 

0 

8.5 






— 70 

00 

0.312 

—0.384 

0 

14.5 

32.548 

10766 

13 

29 

250 

—200 

200 

0.713 

—0.739 

—0.739 

0 

36.565 

13177 

—3774 

30 

250 

200 

200 

0.713 

0.739 

0.739 

0 

36.576 

13181 

3842 

31 

250 

200 

200 

0.713 

0.739 

0.739 

0 






70 

70 

0.363 

0.384 

0.384 

8.5 






— 70 

— 70 

0.363 

—0.384 

—0.384 

14 

32.470 

9914 

— 15 


- \^CONFIDENTIAi7~^ 


APPENDIX 


221 


RDA No. 120 Edition No. 4 {Continued) 


Run 


No. 

^0 


de 

Cd 





X ( tf ) 

Vitf ) 

33 

250 

20° 

00 

0.487 

0.739 

0 

0 






70 

00 

0.312 

0.384 

0 

8.5 

31.887 

10470 

2152 

70 

250 

70 

70 

0.363 

0.384 

0.384 

8 






70 

— 70 

0.363 

0.384 

—0.384 

20 

32.192 

10734 

1438 

73 

250 

70 

70 

0.363 

0.384 

0.384 

0 






70 

— 70 

0.363 

0.384 

—0.384 

20 

32.634 

10828 

1828 

75. 











76 

250 

70 

70 

0.363 

0.384 

0.384 

8 






70 

— 70 

0.363 

0.384 

—0.384 

23 

32.434 

11186 

1468 

77 

250 

70 

70 

0.363 

0.384 

0.384 

8 






70 

— 70 

0.363 

0.384 —0.384 

17 

31.956 

10304 

1402 

87 

250 

70 

70 

0.363 

0.384 

0.384 

8 






70 

00 

0.312 

0.384 

0 

15 






70 

— 70 

0.363 

0.384 

—0.384 

23 

32.020 

10626 

1424 

90 

253.8 

70 

70 

0.363 

0.384 

0.384 

8 





(10° 











Glide) 

70 

— 70 

0.363 

0.384 

—0.384 

20 

30.286 

10310 

1356 

140 

250 

70 

00 

0.312 

0.384 

0 

8 






- 7C 

00 

0.312 

—0.384 

0 

19 

31.678 

10696 

19 

143 

250 

200 

00 

0.487 

0.739 

0 

8 






-200 

00 

0.487 

—0.739 

0 

19.5 

32.303 

10522 

122 

144 

250 

200 

00 

0.487 

0.739 

0 

8 






-200 

00 

0.487 

—0.739 

0 

19 

32.325 

10530 

— 19 

146 

250 

00 

00 

0.261 

0 

0 


31.487 

10745 

0 

147 

250 

00 

70 

0.312 

0 

0.384 

8 






00 

— 70 

0.312 

0 

—0.384 

19 

31.848 

10651 

0 

148 

250 

00 

— 70 

0.312 

0 

—0.384 

8 






00 

70 

0.312 

0 

0.384 

19 

31.502 

10724 

0 

141 

175 

70 

00 

0.312 

0.384 

0 

8 






- 70 

00 

0.312 

—0.384 

0 

19 

31.579 

7544 

— 60 

142 

175 

70 

00 

0.312 

0.384 

0 

8 






- 70 

00 

0.312 

—0.384 

0 

19.5 

31.578 

7544 

9 

149 

175 

00 

— 70 

0.312 

0 

—0.384 

8 






00 

70 

0.312 

0 

0.384 

19 

31.487 

7634 

0 

150 

175 

00 

70 

0.312 

0 

0.384 

8 






00 

— 70 

0.312 

0 

—0.384 

19 

31.674 

7449 

0 

151 

175 

00 

00 

0.261 

0 

0 


31.405 

7576 

0 

88 

175 

70 

70 

0.363 

0.384 

0.384 

8 






70 

— 70 

0.363 

0.384 

—0.384 

20 

31.975 

7539 

1223 


RDA No. 120 Edition No. 5. Initial Altitude 15,000 feet. 
1,000-pound Razon 
(R. D. Wyckoff Coefficients, 12-21-43) 


Run 


No. 

^0 

dg 

5b 

Cx, 

Cs 

Cl 


tf 

X{tf) 

Vitf) 

3 

175 

0° 

00 

0.262 

0 

0 

0 

31.739 

7475 

0 

102 

175 

00 

— 20 

0.264 

0 

—0.093 

0 

31.520 

7030 

0 

103 

175 

00 

20 

0.264 

0 

0.093 

0 

32.010 

7934 

0 

98 

175 

0° 

— 5 

0.286 

0 

—0.216 

0 

31.350 

6429 

0 

99 

175 

00 

50 

0.286 

0 

0.216 

0 

32.494 

8630 

0 

94 

175 

00 

— 80 

0.334 

0 

—0.320 

0 

31.362 

5888 

0 

95 

175 

00 

80 

0.334 

0 

6.320 

0 

33.120 

9033 

0 

90 

175 

00 

—100 

0.371 

0 

—0.382 

0 

31.435 

5595 

0 

91 

175 

0° 

100 

0.371 

0 

0.382 

0 

33.491 

9280 

0 

114 

175 

20 

00 

0.264 

0.093 

0 

0 

31.762 

7473 

474 

111 

175 

50 

00 

0.286 

0.216 

0 

0 

31.911 

7437 

1100 

110 

175 

80 

00 

0.334 

0.324 

0 

0 

32.201 

7363 

1639 

108 

175 

100 

00 

0.371 

0.382 

0 

0 

32.422 

7307 

1926 

85 

175 

— 20 

— 20 

0.266 

—0.093 

—0.093 

0 

31.538 

7024 

— 479 

86 

175 

20 

20 

0.266 

0.093 

0.093 

0 

32.029 

7929 

496 

81 

175 

— 50 

— 50 

0.310 

—0.216 

—0.216 

0 

31.516 

6396 

—1067 

82 

175 

50 

50 

0.310 

0.216 

0.216 

0 

32.665 

8483 

1160 

77 

175 

— 80 

— 80 

0.406 

—0.324 

—0.324 

0 

31.820 

5802 

—1662 


RDA No. 120 Edition No. 5 {Continued) 


Run 

No. 

^0 

Sk 

Se 

Cx, 

Cb 


h 


X(tf) 

y(tf) 

78 

175 

80 

80 

0.406 

0.324 

0.324 

0 

33.558 

8876 

1743 

72 

175 

—100 

—100 

0.480 

—0.382 

—0.382 

0 

32.111 

6471 

—1812 

73 

175 

10° 

100 

0.480 

0.382 

0.382 

0 

34.174 

9046 

2051 

58 

175 

00 

200 

0.580 

0 

0.637 

8 

35.007 

10196 

0 

59 

175 

00 

—200 

0.580 

0 

,—0.637 

8 

32.316 

4731 

0 

60 

175 

0° 

—200 

0.580 

0 

0.637 

15.5 

32.291 

5622 

0 

61 

175 

00 

200 

0.580 

0 

0.637 

15.5 

33.971 

9531 

0 

62 

175 

0° 

200 

0.580 

0 

0.637 

23 

32.620 

8386 

0 

63 

175 

00 

—200 

0.580 

0 

—0.637 

23 

32.013 

6623 

0 

64 

175 

00 

—200 

0.680 

0 

—0.637 

27 

31.841 

7166 

0 

65 

175 

00 

200 

0.580 

0 

0.637 

27 

32.031 

7803 

0 

66 

175 

200 

00 

0.580 

0.637 

0 

8 

33.514 

7188 

2653 

67 

175 

200 

00 

0.580 

0.637 

0 

15.5 

33.038 

7347 

1939 

68 

175 

200 

00 

0.580 

0.637 

0 

23 

32.292 

7451 

854 

69 

175 

200 

00 

0.580 

0.637 

0 

27 

31.932 

7613 

309 

43 

175 

200 

200 

0.898 

0.637 

0.637 

8 

36.822 

9646 

2908 

44 

175 

—200 

—200 

0.898 

—0.637 

—0.637 

8 

33.743 

4575 

—2416 

45 

175 

—200 

—200 

0.898 

—0.637 

—0.637 

15.5 

33.586 

5464 

—1794 

46 

175 

200 

200 

0.898 

0.637 

0.637 

15.5 

36.377 

9260 

2109 

48 

175 

200 

200 

0.898 

0.637 

0.637 

23 

33.228 

8332 

913 

49 

175 

—200 

—200 

0.898 

—0.637 

—0.637 

23 

32.583 

6611 

— 811 

50 

175 

—200 

—200 

0.898 

—0.637 

—0.637 

27 

32.032 

7162 

— 301 

51 

175 

200 

200 

0.898 

0.637 

0.637 

27 

32.236 

7795 

323 

28 

250 

00 

00 

0.262 

0 

0 


31.853 

10676 

0 

100 

250 

00 

20 

0.264 

0 

0.093 

0 

32.290 

11140 

0 

101 

250 

— 00 

— 20 

0.264 

0 

—0.093 

0 

31.481 

10025 

0 

96 

250 

00 

50 

0.286 

0 

0.216 

0 

33.019 

11871 

0 

97 

250 

— 00 

— 50 

0.286 

0 

—0.216 

0 

31.136 

9292 

0 

92 

250 

00 

80 

0.334 

0 

0.320 

0 

33.869 

12469 

0 

93 

250 

— 00 

— 80 

0.334 

0 

0.320 

0 

31.024 

8629 

0 

87 

250 

00 

100 

0.480 

0 

0.382 

0 

34.405 

12759 

0 

88 

250 

00 

—100 

0.480 

0 

—0.382 

0 

31.041 

8269 

0 

113 

250 

20 

00 

0.264 

0.093 

0 

0 

31.880 

10669 

596 

136 

250 

60 

00 

0.286 

0.216 

0 

0 

32^049 

10504 

1398 

109 

250 

80 

00 

0.334 

0.324 

0 

0 

32^378 

10376 

2047 

104 

250 

100 

00 

0.371 

0.382 

0 

0 

32.644 

10286 

2404 

83 

250 

20 

20 

0.266 

0.093 

0.093 

0 

32.316 

11132 

625 

84 

250 

— 20 

— 20 

0.266 

—0.093 

—0.093 

0 

31.524 

10025 

— 595 

79 

250 

50 

50 

0.310 

0.216 

0.216 

0 

33.217 

11788 

1478 

80 

250 

— 50 

— 50 

0.310 

—0.216 

—0.216 

0 

31.327 

9235 

—1312 

74 

250 

80 

80 

0.406 

0.324 

0.324 

0 

34.385 

12197 

2227 

75 

250 

— 80 

— 80 

0.406 

—0.324 

—0.324 

0 

31.541 

8481 

—1889 

70 

250 

100 

100 

0.480 

0.382 

0.382 

0 

35.145 

12337 

2611 

71 

250 

—100 

—100 

0.480 

—0.382 

—0.382 

0 

31.798 

8057 

—2176 

19 

250 

00 

200 

0.680 

0 

0.637 

8 

36.204 

13765 

0 

21 

250 

00 

—200 

0.680 

0 

—0.637 

8 

31.991 

7415 

0 

22 

250 

00 

—200 

0.580 

0 

—0.637 

15.5 

32.134 

8405 

0 

23 

250 

00 

200 

0.580 

0 

0.637 

15.5 

34.695 

12937 

0 

24 

250 

00 

200 

0.580 

0 

0.637 

23 

32.940 

11604 

0 

25 

250 

00 

—200 

0.580 

0 

—0.637 

23 

32.024 

9642 

0 

26 

250 

00 

—200 

0.580 

0 

—0.637 

27 

31.927 

10231 

0 

27 

250 

00 

200 

0.580 

0 

0.637 

27 

32.210 

10946 

0 

38 

250 

200 

00 

0.680 

0.637 

0 

8 

33.800 

10117 

3104 

39 

250 

200 

00 

0.580 

0.637 

0 

15.5 

33.236 

10378 

2148 

40 

250 

200 

00 

0.580 

0.637 

0 

23 

32.452 

10539 

927 

41 

250 

200 

00 

0.580 

0.637 

0 

27 

32.056 

10568 

339 

29 

250 

200 

200 

0.898 

0.637 

0.637 

0 

39.075 

12543 

4150 

30 

250 

200 

200 

0.898 

0.637 

0.637 

8 

38.113 

12875 

3457 

31 

250 

—200 

—200 

0.898 

—0.637 

—0.637 

8 

33.874 

7171 

—2693 

32 

250 

—200 

—200 

0.898 

—0.637 

—0.637 

15.5 

33.484 

8302 

—1912 

33 

250 

200 

200 

0.898 

0.637 

0.637 

15.5 

36.194 

12559 

2419 

34 

250 

200 

200 

0.898 

0.637 

0.637 

23 

33.591 

11526 

1019 

35 

250 

—200 

—200 

0.898 

—0.637 

—0.637 

23 

32.629 

9622 

— 859 

36 

250 

—200 

—200 

0.898 

—0.637 

—0.637 

27 

32.124 

10225 

— 324 

37 

250 

200 

200 

0.898 

0.637 

0.637 

27 

32.434 

10933 

360 

4 

250 

80 

80 

0.406 

0.324 

0.324 

8 






80 

— 8 ° 

0.406 

0.324 

—0.324 

20 

32.918 

10451 

1632 


CONFIDENTIAL 




222 


APPENDIX 


RDA No. 120 Edition No. 5 {Continued) 


Run 

No. 

^0 

5r 

bE 




*1 



y(tf) 

6 

250 

8° 

80 

0.406 

0.324 

0.324 

8 






8° 

— 80 

0.406 

0.324 

—0.324 

20.5 

32.990 

10523 

1633 

7-8 

250 

80 

80 

0.406 

0.324 

0.324 

8 






8° 

— 80 

0.406 

0.324 

—0.324 

23.5 

33.254 

11010 

1673 

9 

175 

80 

80 

0.406 

0.324 

0.324 

8 






80 

— 80 

0.406 

0.324 

—0.324 

20.5 

32.678 

7425 

1399 

55 

250 

200 

OO 

0.580 

0.637 

0 

8 






—200 

OO 

0.580 

—0.637 

0 

19 

33.419 

10164 

— 105 

56 

250 

200 

OO 

0.580 

0.637 

0 

8 






—200 

OO 

0.580 

—0.637 

0 

20 

33.417 

10165 

203 

119 

250 

200 

OO 

0.580 

0.637 

0 

0 






—200 

OO 

0.580 

—0.637 

0 

12 






OO 

OO 

0.262 

0 

0 

20 

32.671 

9929 

95 

120 

250 

200 

OO 

0.580 

0.637 

0 

0 






—200 

OO 

0.580 

—0.637 

0 

11 






OO 

OO 

0.262 

0 

0 

20 

32.677 

9931 

— 142 

121 

250 

200 

OO 

0.580 

0.637 

0 

0 






—200 

OO 

0.580 

—0.637 

0 

11.6 






OO 

OO 

0.262 

0 

0 

20 

32.672 

9931 

9 

122 

250 

OO 

—200 

0.580 

0 

—0.637 

0 

31.454 

6715 

0 

123 

250 

OO 

—200 

0.580 

0 

—0.637 

0 






OO 

OO 

0.262 

0 

0 

20 

31.008 

7895 

0 

125 

250 

OO 

—200 

0.580 

0 

—0.637 

0 






OO 

OO 

0.262 

0 

0 

21 

31.039 

7722 

0 

126 

250 

OO 

—200 

0.580 

0 

—0.637 

0 






OO 

200 

0.580 

0 

0.637 

21 

32.020 

8780 

0 

130 

250 

OO 

— 80 

0.334 

0 

—0.324 

8 






OO 

80 

0.334 

0 

0.324 

20 

31.921 

10357 

0 

131- 











132 

250 

OO 

— 80 

0.334 

0 

—0.324 

8 






OO 

80 

0.334 

0 

0.324 

19.5 

31.965 

10445 

0 

133 

250 

OO 

— 80 

0.334 

0 

—0.324 

8 






OO 

80 

0.334 

0 

0.324 

19 

32.019 

10538 

0 

134 

175 

OO 

— 80 

0.334 

0 

—0.324 

8 






OO 

80 

0.334 

0 

0.324 

19 

31.972 

7540 

0 

135 

175 

OO 

— 80 

0.334 

0 

—0.324 

8 






OO 

80 

0.334 

0 

0.324 

19.5 

31.936 

7458 

0 


RDA No. 120 

Edition No. 6. Initial Altitude 15,000 feet. 
1,000-pound Razon 

Effect of increase in 

Run 

No. 

^0 

Sr 

Se 




h 

C 

x(tf) y(tf) 

1 

250 

0° 

OO 

0.524 

0 

0 


33.164 

10003 

0 

2 

250 

80 

80 

0.668 

0.324 

0.324 

8 






80 - 

-80 

0.668 

0.324 

—0.324 

20.5 

34.248 

9880 

1534 

3 

250 

80 

80 

0.668 

0.324 

0.324 

8 






80 - 

-80 

0.668 

0.324 

—0.324 

21 

34.289 

9952 

1538 

4 

250 

OO - 

-80 

0.596 

0 

—0.324 

8 

32.696 

8479 

0 


RDA No. 119 

(R. 

Edition No. 7. Initial Altitude 28,000 feet. 
1,000-pound Razon 

D. Wyckoff Coefficients, 12-21-43) 

Run 

No. 

^0 

Sr 

Se 




h 

tf 

X(tf) 

yitf) 

1 

250 

OO 

OO 

0.262 

0 

0 


44.205 

14332 

0 

3 

250 

80 

80 

0.406 

0.324 

0.324 

8 






80 — 

80 

0.406 

0.324 

—0.324 

30 

46.616 

14429 

4128 

4 

250 

OO 

80 

0.334 

0 

0.324 

8 






OO — 

80 

0.334 

0 

—0.324 

30 

45.106 

14653 

0 


RDA No. 119 Edition No. 7 {Continued) 


Run 










No. 

^0 Sr 

Se 





X (t,) 

yUf) 

5 

250 0° 

8° 

0.334 0 

0.324 


8 





0° — 

8° 

0.334 0 

—0.324 

29 

45.011 

14354 

0 

6 

250 0° — 

80 

0.334 0 

—0.324 


8 

43.374 

10236 

0 

7 

250 OO 

80 

0.334 0 

0.324 


0 





OO — 

80 

0.334 0 

—0.324 

29 

45.333 

14413 

0 

13 

250 OO 200 

0.580 0 

0.637 


0 





OO — 

80 

0.334 0 

i —0.324 

20 

46.262 

12502 

0 

14 

250 OO —200 

0.580 0 

—0.637 


0 





OO — 

80 

0.334 0 

1 —0.324 

20 

43.629 

8523 

0 

15 

250 OO 200 

0.580 0 

i 0.637 


0 





OO — 

80 

0.334 0 —0.324 


25 

47.201 

13966 

0 

16 

250 OO 200 

0.580 0 

1 0.637 


0 





OO — 

80 

0.334 0 —0.324 


26.5 

47.509 

14462 

0 

17 

250 OO 200 

0.580 0 

1 0.637 


0 





OO — 

80 

0.334 0 —0.324 


26 

47.438 

14303 

0 

8 

175 OO 

80 

0.334 0 0.324 


8 ' 





OO — 

80 

0.334 0 —0.324 


29 

45.126 

10194 

0 

9 

175 OO 

OO 

0.262 0 0 


0 

44.073 

10119 

0 

10 

175 80 

80 

0.406 0.324 0.324 


8 





80 — 

80 

0.406 0.324 —0.324 


30 

46.173 

10252 

0 

11 

175 OO — 

80 

0.334 0 — 0.324 


8 

44.107 

6438 

0 

RDA No. 120 

Edition No. 8. Initial Altitude 15,000 feet. 




1,000-pound Razon 






(Synthetic Coefficients) 



Run 










No. 

^0 P'-P'-Cd Cd 


Ce < 

•1 



X(tf) 

yitf) 

1 

250 0.2 

0.2 

0 

0 



31.545 

10710 

0 

6 

250 0.2 

0.5 

0 

0.55 

8 


35.271 

13430 

0 

7 

250 0.2 

0.5 

0 

—0.55 

8 


31.717 

7892 

0 

10 

250 0.2 

0.5 

0 

0.55 23 


32.469 

11585 

0 

11 

250 0.2 

0.5 

0 

—0.55 23 


31.714 

9911 

0 

13 

250 0.2 

0.5 

0 

0.75 

8 


36.656 

14896 

0 

14 

250 0.2 

0.5 

0 

—0.75 

8 


31.446 

7048 

0 

19 

250 0.2 

0.5 

0 

—0.75 23 


31.645 

9645 

0 

20 

250 0.2 

0.5 

0 • 

0.75 23 


32.715 

11966 

0 

21 

250 0.2 

0.7 

0 

0.55 

8 


36.154 

12995 

0 

22 

250 0.2 

0.7 

0 

—0.55 

8 


32.610 

7738 

0 

28 

250 0.2 

0.7 

0 

0.55 23 


32.799 

11549 

0 

29 

250 0.2 

0.7 

0 

—0.55 23 


32.005 

9895 

0 

30 

250 0.2 

0.7 

0 

—0.75 23 


31.936 

9633 

0 

31 

250 0.2 

0.7 

0 

0.75 23 


33.052 

11920 

0 

36 

250 0.2 

0.7 

0 

0.75 

8 


37.481 

14317 

0 

37 

250 0.2 

0.7 

0 

—0.75 

8 


32.360 

6922 

0 

97 

250 0.2 

0.5 

0.55 

0 23 


32.059 

10682 

792 

100 

250 0.2 

0.5 

0.55 

0 

8 


33.289 

10295 

2722 

102 

250 0.2 

0.5 

0.75 

0 23 


33.616 

10245 

3754 

105 

250 0.2 

0.5 

0.75 

0 23 


32.117 

10679 

1083 

106 

250 0.2 

0.7 

0.55 

0 

8 


34.196 

10058 

2616 

109 

250 0.2 

0.7 

0.55 

0 23 


32.368 

10659 

2319 

110 

250 0.2 

0.7 

0.75 

0 

8 


34.521 

10011 

3609 

113 

250 0.2 

0.7 

0.75 

0 23 


32.427 

10656 

1074 

42 

250 0.3 

0.3 

0 

0 



32.043 

10485 

0 

40 

250 0.3 

0.5 

0 

0.55 23 


32.834 

11379 

0 

43 

250 0.3 

0.5 

0 

—0.55 23 


32.072 

9675 

0 

47 

250 0.3 

0.5 

0 

0.55 

8 


35.281 

13311 

0 

48 

250 0.3 

0.5 

0 

—0.55 

8 


31.759 

7797 

0 

50 

250 0.3 

0.5 

0 

—0.75 23 


32.010 

9404 

0 

53 

250 0.3 

0.5 

0 

0.75 23 


33.079 

11761 

0 

54 

250 0.3 

0.5 

0 

—0.75 

8 


31.511 

6964 

0 

57 

250 0.3 

0.5 

0 

0.75 

8 


36.627 

14747 

0 

58 

250 0.3 

0.7 

0 

—0.55 23 


32.381 

9660 

0 


* rONFIDENTIAL 


APPENDIX 


223 


RDA No. 120 Edition No. 8 {Continued) RDA No. 120 Edition No. 8 {Continued) 

~ (Coefficients for Line of Sight Control) 


No . 

^0 

F . F . C ^ 




<1 

C 

Xitf) 

y(tf) 

Run 










61 

250 

0.3 

0.7 

0 

0.55 

23 

33.174 

11341 

0 

No . 

^0 



Cr. 

<1 

if 

X (tf) 

v(tf) 

62 

250 

0.3 

0.7 

0 

0.55 

8 

36.163 

12882 

0 











65 

250 

0.3 

0.7 

0 

— 0.55 

8 

32.667 

7653 

0 

114 

250 

0.2 

0.2 

0 

0 


31.543 

10718 

0 

66 

250 

0.3 

0.7 

0 

— 0.75 

23 

32.315 

9360 

0 

115 

250 

0.2 

0.8 

0.75 

0.75 

8 




69 

250 

0.3 

0.7 

0 

0.75 

23 

33.432 

11718 

0 




0.8 

0.75 

— 0.75 

19 

35.581 

9501 

3603 

71 

250 

0.3 

0.7 

0 

0.75 

8 

37.505 

14191 

0 

116 

250 

0.2 

0.8 

0.75 

0.75 

8 




74 

250 

0.3 

0.7 

0 

— 0.75 

8 

32.422 

6838 

0 




0.8 

0.75 

— 0.75 

22 

36.166 

10371 

3733 

79 

250 

0.3 

0.5 

0.55 

0 

8 

33.326 

10195 

2709 

117 

250 

0.2 

0.8 

0.75 

0.75 

8 




82 

250 

0.3 

0.5 

0.55 

0 

23 

32.422 

10463 

808 




0.8 

0.75 

— 0.75 

23.5 

36.459 

10806 

3806 

85 

250 

0.3 

0.5 

0.75 

0 

23 

32.489 

10460 

1109 

119 

250 

0.2 

0.6 

0.75 

0.75 

8 




86 

250 

0.3 

0.5 

0.75 

0 

8 

33.649 

10146 

3730 




0.6 

0.75 

— 0.75 

22 

35.296 

10725 

3918 

89 

250 

0.3 

0.7 

0.55 

0 

8 

34.232 

9961 

2603 

123 

250 

0.3 

0.51 

0.79 

0.79 

8 




90 

250 

0.3 

0.7 

0.55 

0 

23 

32.744 

10439 

799 




0.51 

0.79 

— 0.79 

20.25 

34.689 

10183 

4094 

93 

250 

0.3 

0.7 

0.75 

0 

23 

32.806 

10435 

1096 

125 

250 

0.3 

0.51 

0.79 

0.79 

8 




94 

250 

0.3 

0.7 

0.75 

0 

8 

34.550 

9915 

3584 




0.51 

0.79 

— 0.79 

23 

35.290 

11117 

4274 

2 

175 

0.2 

0.2 

. 0 

0 


31.456 

7560 

0 

126 

250 

0.3 

0.51 

0.79 

0.79 

8 




5 

175 

0.2 

0.5 

0 

0.55 

23 

32.235 

8334 

0 




0.51 

0.79 

— 0.79 

21.2 

34.894 

10504 

4151 

8 

175 

0.2 

0.5 

0 

— 0.55 

8 

32.009 

5133 

0 











9 

175 

0.2 

0.5 

0 

0.55 

8 

34.300 

9888 

0 

127 

250 

0.3 

0.3 

0 

0 


32.042 

10489 

0 

12 

175 

0.2 

0.5 

0 

— 0.55 

23 

31.705 

6829 

0 

128 

250 

0.3 

0.61 

1.19 

1.19 

8 

















0.61 

1.19 

— 1.19 

21.2 

37.177 

10108 

6526 

15 

175 

0.2 

0.5 

0 

— 0.75 

8 

31.896 

4361 

0 











16 

175 

0.2 

0.5 

0 

0.75 

8 

35.200 

11022 

0 

129 

250 

0.3 

0.61 

1.19 

1.19 

8 




17 

175 

0.2 

0.5 

0 

0.75 

23 

32.387 

8652 

0 




0.61 

1.19 

— 1.19 

22.2 

37.505 

10544 

6653 

18 

175 

0.2 

0.5 

0 

— 0.75 

23 

31.674 

6577 

0 

130 

250 

0.3 

0.4 

0 

0.79 

8 




24 

175 

0.2 

0.7 

0 

0.55 

8 

35.162 

9620 

0 




0.4 

0 

— 0.79 

19.5 

33.230 

10241 

0 

25 

175 

0.2 

0.7 

0 

— 0.55 

8 

32.866 

5044 

0 

131 

250 

0.3 

0.4 

0 

0.79 

8 




26 

175 

0.2 

0.7 

0 

— 0.55 

23 

31.992 

6820 

0 




0.4 

0 

— 0.79 

20.5 

33.437 

10607 

0 

27 

175 

0.2 

0.7 

0 

0.55 

23 

32.520 

8305 

0 

132 

250 

0.3 

0.4 

0 

0.79 

8 




32 

175 

0.2 

0.7 

0 

0.75 

23 

32.699 

8621 

0 




0.4 

0 

— 0.79 

20.2 

33.372 

10497 

0 

33 

175 

0.2 

0.7 

0 

— 0.75 

23 

31.959 

6569 

0 

133 

250 

0.3 

0.4 

0 

— 0.79 

8 




34 

175 

0.2 

0.7 

0 

— 0.75 

8 

32.758 

4291 

0 




0.3 

0 

0 

20 

30.184 

7540 

0 

35 

175 

0.2 

0.7 

0 

0.75 

8 

36.036 

10672 

0 

135 

250 

0.3 

0.4 

0 

— 0.79 

0 




98 

175 

0.2 

0.5 

0.55 

0 

23 

31.944 

7538 

728 




0.3 

0 

0 

20 

30.184 

7537 

0 

99 

175 

0.2 

0.5 

0.55 

0 

8 

33.053 

7297 

2350 



n Q 

il A 

A 

1 1 Q 

A 




103 

175 

0.2 

0.5 

0.75 

0 

8 

33.331 

7268 

3239 

loo 


u.o 

U.400 



u 

















0.456 

0 

— 1.19 

22 

36.260 

11151 

0 

104 

175 

0.2 

0.5 

0.75 

0 

23 

31.996 

7536 

998 

137 

250 

0.3 

0.456 

0 

1.19 

0 




107 

175 

0.2 

0.7 

0.55 

0 

8 

33.913 

7148 

2275 




0.456 

0 

— 1.19 

21 

35.978 

10670 

0 

108 

175 

0.2 

0.7 

0.55 

0 

23 

32.237 

7523 

721 











111 

175 

0.2 

0.7 

0.75 

0 

8 

34.189 

7118 

3133 

138 

250 

0.3 

0.456 

0 

1.19 

0 




112 

175 

0.2 

0.7 

0.75 

0 

23 

32.292 

7521 

988 




0.456 

0 

— 1.19 

20.4 

35.786 

10384 

0 











139 

250 

0.3 

0.456 

0 

— 1.19 

0 




39 

175 

0.3 

0.3 

0 

0 


31.915 

7426 

0 




0.3 

0 

0 

25 

29.801 

4832 

0 

44 

175 

0.3 

0.5 

0 

— 0.55 

23 

32.037 

6682 

0 











45 

175 

0.3 

0.5 

0 

0.55 

23 

32.546 

8215 

0 











46 

175 

0.3 

0.5 

0 

0.55 

8 

34.316 

9821 

0 











49 

175 

0.3 

0.5 

0 

— 0.55 

8 

32.049 

5082 

0 











51 

175 

0.3 

0.5 

0 

— 0.75 

23 

32.005 

6425 

0 

RDA No. 

120 

Edition No. 9. Initial Altitude 15,000 feet. 

52 

175 

0.3 

0.5 

0 

0.75 

23 

32.719 

8540 

0 





2,000-pound Razon 




55 

175 

0.3 

0.5 

0 

— 0.75 

8 

31.945 

4309 

0 




(Synthetic Coefficients) 



56 

175 

0.3 

0.5 

0 

0.75 

8 

35.207 

10949 

0 











59 

175 

0.3 

0.7 

0 

— 0.55 

23 

32.333 

6673 

o’ 

Run 










60 

175 

0.3 

0.7 

0 

0.55 

23 

32.863 

8190 

0 

No . 

^0 

F . F . C ^ 


Cl 



X{tf) 

y(tf) 

63 

175 

0.3 

0.7 

0 

0.55 

8 

35.181 

9558 

0 

1 

250 

0.2 

0.2 

0 

0 


31.266 

10847 

0 

64 

175 

0.3 

0.7 

0 

— 0.55 

8 

32.911 

4991 

0 

6 

250 

0.2 

0.5 

0 

0.55 

8 

33.808 

12805 

0 

67 

175 

0.3 

0.7 

0 

0.75 

23 

32.300 

6418 

0 

10 

250 

0.2 

0.5 

0 

— 0.55 

8 

31.290 

8708 

0 

68 

175 

0.3 

0.7 

0 

0.75 

23 

33.045 

8511 

0 

11 

250 

0.2 

0.5 

0 

— 0.55 

23 

31.358 

10261 

0 

72 

175 

0.3 

0.7 

0 

0.75 

8 

36.050 

10606 

0 

14 

250 

0.2 

0.5 

0 

0.55 

23 

31.885 

11457 

0 

73 

175 

0.3 

0.7 

0 

— 0.75 

8 

32.809 

4234 

0 

15 

250 

0.2 

0.5 

0 

0.75 

8 

34.602 

13774 

0 

75 

175 

0.3 

0.7 

0 

— 0.75 

23 

32.299 

6419 

0 

18 

250 

0.2 

0.5 

0 

— 0.75 

8 

31.052 

8071 

0 

80 

175 

0.3 

0.5 

0.55 

0 

8 

33.087 

7239 

2348 

19 

250 

0.2 

0.5 

0 

— 0.75 

23 

31.308 

10068 

0 

81 

175 

0.3 

0.5 

0.55 

0 

23 

32.274 

7408 

745 

22 

250 

0.2 

0.5 

0 

0.75 

23 

32.029 

11712 

0 

84 

175 

0.3 

0.5 

0.75 

0 

23 

32.329 

7407 

1019 

23 

250 

0.2 

0.7 

0 

0.55 

8 

34.471 

12531 

0 

87 

175 

0.3 

0.5 

0.75 

0 

8 

33.362 

7212 

3231 

26 

250 

0.2 

0.7 

0 

— 0.55 

8 

31.954 

8586 

0 

88 

175 

’ 0.3 

0.7 

0.55 

0 

8 

33.944 

7089 

2276 

27 

250 

0.2 

0.7 

0 

— 0.55 

23 

31.572 

10250 

0 

91 

175 

0.3 

0.7 

0.55 

0 

23 

32.580 

7393 

737 

30 

250 

0.2 

0.7 

0 

0.55 

23 

32.107 

11434 

0 

92 

175 

0.3 

0.7 

0.75 

0 

23 

32.637 

7390 

1013 

31 

250 

0.2 

0.7 

0 

0.75 

23 

32.254 

11685 

0 

95 

175 

0.3 

0.7 

0.75 

0 

8 

34.220 

7063 

3128 

34 

350 

0.2 

0.7 

0 

— 0.75 

23 

31.513 

10055 

0 


^^ONFIDENTIA’ 


224 


APPENDIX 


RDA No. 120 Edition No. 9 {Continued) 


Run 


No. 

^0 

F.F.C^ 

Cn 


Ct 

*1 

if 

Xltf) 

yitf) 

35 

250 

0.2 

0.7 

0 

—0.75 

8 

31.702 

7968 

0 

38 

250 

0.2 

0.7 

0 

0.75 

8 

35.252 

13452 

0 

40 

250 

0.2 

0.5 

0.55 

0 

8 

32.451 

10547 

2010 

43 

250 

0.2 

0.5 

0.55 

0 

23 

31.610 

10824 

565 

44 

250 

0.2 

0.5 

0.75 

0 

8 

32.620 

10521 

2762 

47 

250 

0.2 

0.5 

0.75 

0 

23 

31.640 

10823 

772 

48 

250 

0.2 

0.5 

0.55 

0 

8 

33.112 

10371 

1956 

51 

250 

0.2 

0.5 

0.55 

0 

23 

31.825 

10808 

565 

52 

250 

0.2 

0.5 

0.75 

0 

8 

32.606 

10192 

2565 

55 

250 

0.2 

0.5 

0.75 

0 

23 

31.853 

10807 

767 

56 

250 

0.3 

0.3 

0 

0 


31.627 

10680 

0 

59 

250 

0.3 

0.5 

0 

0.55 

23 

32.150 

11304 

0 

65 

250 

0.3 

0.5 

0 

0.55 

8 

33.820 

12715 

0 

66 

250 

0.3 

0.5 

0 

—0.55 

8 

31.335 

8652 

0 

67 

250 

0.3 

0.5 

0 

—0.55 

23 

31.631 

10092 

0 

69 

250 

0.3 

0.5 

0 

—0.75 

8 

31.095 

8012 

0 

71 

250 

0.3 

0.5 

0 

—0.75 

23 

31.574 

9894 

0 

72 

250 

0.3 

0.5 

0 

0.75 

23 

32.296 

11562 

0 

75 

250 

0.3 

0.5 

0 

0.75 

8 

34.602 

13674 

0 

76 

250 

0.3 

0.7 

0 

0.55 

8 

34.479 

12445 

0 

79 

250 

0.3 

0.7 

0 

0.55 

23 

32.379 

11281 

0 

80 

250 

0.3 

0.7 

0 

—0.55 

23 

31.841 

10080 

0 

83 

250 

0.3 

0.7 

0 

—0.55 

8 

31.989 

8522 

0 

84 

250 

0.3 

0.7 

0 

—0.75 

8 

31.746 

7905 

0 

87 

250 

0.3 

0.7 

0 

—0.75 

23 

31.783 

9885 

0 

88 

250 

0.3 

0.7 

0 

0.75 

23 

32.530 

11535 

0 

91 

250 

0.3 

0.7 

0 

0.75 

8 

35.251 

13349 

0 

92 

250 

0.3 

0.5 

0.55 

0 

8 

32.481 

10474 

2005 

96 

250 

0.3 

0.5 

0.55 

0 

23 

31.875 

10664 

572 

97 

250 

0.3 

0.5 

0.75 

0 

8 

32.648 

10448 

2742 

100 

250 

0.3 

0.5 

0.75 

0 

23 

31.904 

10662 

784 

101 

250 

0.3 

0.7 

0.55 

0 

23 

32.095 

10648 

569 

104 

250 

0.3 

0.7 

0.55 

0 

8 

33.142 

10301 

1948 

105 

250 

0.3 

0.7 

0.75 

0 

8 

33.308 

10275 

2677 

108 

250 

0.3 

0.7 

0.75 

0 

23 

32.123 

10646 

778 

2 

175 

0.2 

0.2 

0 

0 


31.202 

7637 

0 

7 

175 

0.2 

0.5 

0 

0.55 

8 

33.131 

9312 

0 

8 

175 

0.2 

0.5 

0 

—0.55 

8 

31.532 

5832 

0 

12 

175 

0.2 

0.5 

0 

—0.55 

23 

31.362 

7107 

0 

13 

175 

0.2 

0.5 

0 

0.55 

23 

31.707 

8176 

0 

16 

175 

0.2 

0.5 

0 

0.75 

8 

33.653 

10071 

0 

17 

175 

0.2 

0.5 

0 

—0.75 

8 

31.400 

5256 

0 

20 

175 

0.2 

0.5 

0 

—0.75 

23 

31.329 

6927 

0 

21 

175 

0.2 

0.5 

0 

0.75 

23 

31.806 

8391 

0 

24 

175 

0.2 

0.7 

0 

0.55 

8 

33.766 

9141 

0 

25 

175 

0.2 

0.7 

0 

—0.55 

8 

32.147 

5753 

0 

28 

175 

0.2 

0.7 

0 

—0.55 

23 

31.560 

7100 

0 

29 

175 

0.2 

0.7 

0 

0.55 

23 

31.918 

8161 

0 

32 

175 

0.2 

0.7 

0 

0.75 

23 

32.019 

8376 

0 

33 

175 

0.2 

0.7 

0 

—0.75 

23 

31.526 

6919 

0 

36 

175 

0.2 

0.7 

0 

—0.75 

8 

32.012 

5193 

0 

37 

175 

0.2 

0.7 

0 

0.75 

8 

34.279 

9871 

0 

41 

175 

0.2 

0.5 

0.55 

0 

8 

32.286 

7451 

1723 

42 

175 

0.2 

0.5 

0.55 

0 

23 

31.527 

7620 

521 

45 

175 

0.2 

0.5 

0.75 

0 

8 

32.430 

7435 

2365 

46 

175 

0.2 

0.5 

0.75 

0 

23 

31.552 

7620 

709 

49 

175 

0.2 

0.7 

0.55 

0 

8 

32.908 

7339 

1681 

50 

175 

0.2 

0.7 

0.55 

0 

23 

31.730 

7610 

516 

53 

175 

0.2 

0.7 

0.75 

0 

8 

33.047 

7323 

2309 

54 

175 

0.2 

0.7 

0.75 

0 

23 

31.757 

7609 

704 

57 

175 

0.3 

0.3 

0 

0 


31.533 

7538 

0 

61 

175 

0.3 

0.5 

0 

—0.55 

23 

31.603 

7005 

0 

62 

175 

0.3 

0.5 

0 

—0.55 

8 

31.561 

5792 

0 

63 

175 

0.3 

0.5 

0 

0.55 

23 

31.949 

8092 

0 

64 

175 

0.3 

0.5 

0 

0.55 

8 

33.153 

9261 

0 

69 

175 

0.3 

0.5 

0 

—0.75 

8 

31.430 

5222 

0 

70 

175 

0.3 

0.5 

0 

—0.75 

23 

31.569 

6820 

0 

73 

175 

0.3 

0.5 

0 

0.75 

23 

32.051 

8313 

0 

74 

175 

0.3 

0.5 

0 

0.75 

8 

33.658 

10010 

0 

77 

175 

0.3 

0,7 

0 

0.55 

8 

33.783 

9096 

0 


RDA No. 120 Edition No. 9 (Co7itinued) 


Run 


No. 

^0 

F.F.C^ 

Cn 

c. 



tf 

xUf) 

y(tf) 

78 

175 

0.3 

0.7 

0 

0.55 

23 

32.164 

8077 

0 

81 

175 

0.3 

0.7 

0 

—0.55 

23 

31.803 

6997 

0 

82 

175 

0.3 

0.7 

0 

—0.55 

8 

32.175 

5717 

0 

85 

175 

0.3 

0.7 

0 

—0.75 

8 

32.039 

5159 

0 

86 

175 

0.3 

0.7 

0 

—0.75 

23 

31.770 

6814 

0 

89 

175 

0.3 

0.7 

0 

0.75 

23 

32.270 

8296 

0 

90 

175 

0.3 

0.7 

0 

0.75 

8 

34.293 

9825 

0 

93 

175 

0.3 

0.5 

0.55 

0 

8 

32.312 

7409 

1716 

94 

175 

0.3 

0.5 

0.55 

0 

23 

31.769 

7527 

526 

98 

175 

0.3 

0.5 

0.75 

0 

8 

32.456 

7395 

2360 

99 

175 

0.3 

0.5 

0.75 

0 

23 

31.795 

7527 

722 

102 

175 

0.3 

0.7 

0.55 

0 

23 

31.977 

7517 

524 

103 

175 

0.3 

0.7 

0.55 

0 

8 

32.933 

7298 

1686 

106 

175 

0.3 

0.7 

0.75 

0 

8 

33.072 

7282 

2306 

107 

175 

0.3 

0.7 

0.75 

0 

23 

32.004 

7516 

717 


RDA No. 120 Edition No. 10. Initial Velocity 250 mph. 
1,000-pound Azon 

(R. D. Wyckoff Coefficients, 12-21-43) 

Altitude Effects 


Run 

No. 

Altitude 5^ 

Co 

c. 

t, 

if 

X(tf) 

yitf) 

2 

5000 

0° 

0.262 

0 


18.025 

6232 

0 

7 

5000 

20° 

0.580 

0.637 

0 

18.593 

5934 

1003 

13 

5000 

200 

0.580 

0.637 

15.5 

17.997 

6210 

47 

3 

10000 

0° 

0.262 

0 


25.782 

8723 

0 

8 

10000 

200 

0.580 

0.637 

0 

27.104 

8127 

2294 

14 

10000 

200 

0.580 

0.637 

15.5 

26.356 

8640 

825 

1 

15000 

OO 

0.262 

0 


31.853 

10576 

0 

9 

15000 

200 

0.580 

0.637 

0 

34.046 

9753 

3831 

15 

15000 

200 

0.580 

0.637 

15.5 

33.248 

10381 

2151 

19 

15000 

200 

0.580 

0.637 

27 

32.057 

10568 

339 

4 

20000 

OO 

0.262 

0 


37.040 

12153 

0 

10 

20000 

200 

0.580 

0.637 

0 

40.165 

11115 

5548 

16 

20000 

200 

0.580 

0.637 

15.5 

39.382 

11791 

3797 

20 

20000 

200 

0.580 

0.637 

27 

37.901 

12102 

1435 

5 

25000 

OO 

0.262 

0 


41.651 

13554 

0 

11 

25000 

200 

0.580 

0.637 

0 

45.731 

12325 

7375 

17 

25000 

200 

0.580 

0.637 

15.5 

44.970 

13007 

5625 

21 

25000 

200 

0.580 

0.637 

27 

43.387 

13410 

2993 

6 

30000 

OO 

0.262 

0 


45.833 

14831 

0 

12 

30000 

200 

0.580 

0.637 

0 

50.870 

13444 

9286 

18 

30000 

200 

0.580 

0.637 

15.5 

50.252 

14124 

7633 

22 

30000 

200 

0.580 

0.637 

27 

48.571 

14564 

4841 


RDA No, 120 Edition No. 10 {Continued) 
Initial Altitude 15,000 feet. 
Velocity Effects 


Run 

No. 

^0 

5n 

Cn 

c. 

i, 

if 

X {tf) 

yitf) 

23 

175 

OO 

0.262 

0 


31.743 

7477 

0 

28 

175 

200 

0.580 

0.637 

0 

33.703 

6999 

3127 

29 

175 

200 

0.580 

0.637 

15.5 

33.042 

7349 

1943 

24 

250 

OO 

0.262 

0 


31.854 

10574 

0 

27 

250 

200 

0.580 

0.637 

0 

34.048 

9753 

3831 

30 

250 

200 

0.580 

0.637 

15.5 

33.239 

10377 

2151 

54 

325 

OO 

0.262 

0 


31.979 

13601 

0 

56 

325 

200 

0.580 

0.637 

0 

34.445 

12343 

4728 

55 

325 

200 

0.580 

0.637 

15.5 

33.477 

13328 

2422 


*^Ni^DEgTIAU| 


APPENDIX 


225 


RDA No. 120 Edition No. 10 {Continued) 


Run 

No. 

^0 






X(tf) 

y(tf) 




Special Effects 




33 

250 

200 

0.580 

0.637 

0 

34.044 

9754 

3832 

34 

250 

20° 

0.580 

0.637 

0 






-200 

0.580 

—0.637 

10 

33.731 

9835 

—1816 

35 

250 

200 

0.580 

0.637 

0 






-200 

0.580 

—0.637 

15 

33.601 

9828 

— 549 

36 

250 

200 

0.580 

0.637 

0 






-200 

0.580 

—0.637 

20 

33.555 

9804 

900 

37 

250 

200 

0.580 

0.637 

0 






-200 

0.580 

—0.637 

25 

33.667 

9776 

2342 

38 

250 

200 

0.580 

0.637 

0 






OO 

0.262 

0 

10 

32.077 

10149 

1033 

39 

250 

200 

0.580 

0.637 

0 






OO 

0.262 

0 

15 

32.394 

9990 

1663 

40 

250 

200 

0.580 

0.637 

0 






OO 

0.262 

0 

20 

32.844 

9867 

2374 

41 

250 

200 

0.580 

0.637 

0 






OO 

0.262 

0 

25 

33.377 

9791 

3083 

42 

250 

200 

0.580 

0.637 

0 






OO 

0.262 

0 

10 






-200 

0.580 

—0.637 

20 

33.080 

10057 

2474 





Trainer Data 




43 

200 kts 

OO 

0.262 

0 


31.836 

9773 

0 

44 

200 kts 

200 

0.580 

0.637 

15 

33.232 

9578 

2166 

45 

200 kts. 

200 

0.580 

0.637 

0 

33.951 

9046 

3624 





Check Cases 





P 

— = 6 
Po 

>-3.10 X 10-52 . 

A = 1.87 ft2; M = 31.1 slugs 


50 

250 

OO 

0.26 

0 


31.894 

10561 

0 

64 • 

250 

200 

0.58 

0.86 

15 






OO 

0.26 

0 

30 

33.512 

10313 

2949 

65 

250 

200 

0.58 

0.86 

15 

33.711 

10310 

3174 



- 

P 

= e-2.96X 10-52 

« 






Po 






57 

250 

OO 

0.26 

0 


31.909 

10549 

0 

58 

250 

200 

0.58 

0.86 

15 

33.748 

10293 

3199 


RDA No. 121 Edition No. 1. Initial Altitude 15,000 feet. 
2,000-pound Razon 
(R. D. Wyckoff Coefficients, 12-21-43) 

Run 

No. 

Vo 

5e 

Cd 

Cl 

ti 

tf 

Xitf) 

1 

250 

0° 

0.261 

0 


31.485 

10746 

2 

250 

o 

o 

0.487 

0.739 

0 

35.375 

13968 

3 

250 

20° 

0.487 

0.739 

5 





—20° 

0.487 

—0.739 

21 

33.142 

10990 

4 

250 

20° 

0.487 

0.739 

5 





—20° 

0.487 

—0.739 

16 





20° 

0.487 

0.739 

28 

33.447 

10052 

5 

250 

20° 

0.487 

0.739 

5 





—20° 

0.487 

—0.739 

19 





0° 

0.261 

0 

26 





—20° 

0.487 

—0.739 

30 

32.819 

11018 

6 

250 

20° 

0.487 

0.739 

5 





—20° 

0.487 

—0.739 

19 





20° 

0.487 

0.739 

29.5 

32.887 

10781 


RDA No. 121 Edition No. 1 {Continued) 


Run 

No. 

Vo 

ds 

Cn 

Cl 

L 

if 

X{tf) 

9 

250 

20° 

0.487 

0.739 

5 





—20° 

0.487 

—0.739 

21 

33.148 

11021 

10 

250 

20° 

0.487 

0.739 

5 





—20° 

0.487 

—0.739 

20 





20° 

0.487 

0.739 

31.5 

32.985 

10817 

11 

250 

20° 

0.487 

0.730 

5 





—20° 

0.487 

—0.739 

19 





0° 

0.261 

0 

27 

32.821 

10921 

12 

250 

20° 

0.487 

0.739 

5 





—20° 

0.487 

—0.739 

19 





0° 

0.261 

0 

29 

32.824 

10708 

13 

250 

20° 

0.487 

0.739 

0 





—20° 

0.487 

—0.739 

19 





20° 

0.487 

0.739 

30 

33.361 

10780 

14 

250 

20° 

0.487 

0.739 

0 





—20° 

0.487 

—0.739 

21 

33.620 

11027 


Differential Analyzer Trajectories 
FOR Razon 

The following few runs were made at the 
request of Gulf for the purpose of comparison 
with actual tests at Tonopah. Some of the param- 
eters used differ from those of previous dif- 
ferential analyzer solutions. 

M = 1,200 lb 
A = 1.89 ft2 
p/po = 0.765e“^'"* ^ 
po = 0.002378 slug/ft^ 

Vo = 225 mi/hr 

The initial altitude is 15,000 feet. The same 
notation is used as in the other indices. Cg is zero 
for all runs. 

RDA No. 119 Edition No. 4 and 4A. 

Run 


No. 

Cd 

Cl 

L 

tf 

X{tf) 

2 

0.225 

0 


31.286 

9766 

3 

0.34 

—0.36 

0 




0.225 

0 

15.6 




0.340 

—0.36 

17.9 

30.879 

8448 

4 

0.31 

—0.36 

0 




0.225 

0 

15.6 




0.34 

0.36 

17.9 

31.370 

9737 

5 

0.34 

0.36 

0 

32.699 

11064 

6 

0.34 

—0.36 

0 

30.863 

8304 

7 

0.335 

0 


31.649 

9622 

8 

0.627 

—1.0 

0 




0.335 

0 

15.6 




0.627 

—1.0 

17.9 

30815 

6294 

9 

0.627 

—1.0 

0 




0.335 

0 

15.6 




0.627 

1.0 

17.9 

32.006 

9657 

10 

0.627 

1.0 

0 

36.246 

13528 

11 

0.627 

—1.0 

0 

30,834 

5946 


lOlfMDENTIAL 


226 


APPENDIX 


SUPPLEMENTARY INDEX OF DIFFERENTIAL ANALYZER SOLUTIONS 
FOR RAZON TRAJECTORIES 


This index is of data made at the request of 
R. D. Wyckoff for the purpose of studying varia- 
tion in time-of -flight as a result of control. Only 
range control is applied. The same differential 
equations are used as in previous RDA No. 119 
solutions, with full elevator, either up or down, 
applied at the indicated times ti. No allowance 
is made for the time the elevator takes to move 
from neutral position to that of full control, so 
that the aerodynamic coefficients are changed 
discontinuously. Control applied at a time con- 
tinues until a change is made at a new value of 
tif or until impact. Time-of-flight and range-at- 
impact are denoted by tf and x{tf). 

The coefficients used are for the VB-3 Mk II, 
a 1,000-lb Razon model. The parameters used 
are as follows : 

Mass = 1,100 lb 
Area = 1.89sqft 

The density function used is the same as for 
previous trajectories 

/ n nKnx.-2-96Xl0-6^ 

p/pQ = 0.959e 

where 

Po= 0.002378 slug/ft3 
is the density of air at sea level. 


RDA No. 119 Edition No. 8. 
Initial Altitude 15,000 feet. 
Initial Velocity (horizontal) 250 mph. 


Run No. 

Cd 

Cl 

ti (sec) 

tr(sec) 

X{tf) 

1 

0.230 

0 

— 

31.608 

10692 

8 

0.345 

0.430 

0 

34.270 

13049 

2 

0.345 

0.430 

5 

33.889 

12944 

3 

0.345 

0.430 

10 

33.447 

12683 

4 

0.345 

0.430 

15 

32.926 

12247 

5 

0.345 

0.430 

20 

32.376 

11682 

6 

0.345 

0.430 

25 

31.895 

11102 

7 

0.345 

0.430 

30 

31.626 

10722 

9 

0.345 

—0.430 

0 

30.727 

d>2n2, 

10 

0.345 

—0.430 

5 

31.005 

8499 

11 

0.345 

—0.430 

10 

31.225 

8823 

12 

0.345 

—0.430 

15 

31.394 

9257 

13 

0.345 

—0.430 

20 

31.510 

9781 

14 

0.345 

—0.430 

25 

31.577 

10309 

15 

0.345 

—0.430 

30 

31.606 

10662 

16 

0.345 

0.430 

10 




0.230 

0 

15 

32.042 

11078 

17 

0.345 

0.430 

10 




0.230 

0 

20 

32.511 

11679 

18 

0.345 

0.430 

10 




0.230 

0 

25 

32.978 

12122 


RDA No. 119 Edition No. 8 {Continued) 


Run No. Cd 

Cl 

ii(sec) 

if (sec) 

X{tf) 

19 

0.345 

0.430 

10 




0.230 

0 

30 

33.347 

12564 

20 

0.345 

—0.430 

10 




0.230 

0 

15 

31.385 

* 10209 

21 

0.345 

—0.430 

10 




0.230 

0 

20 

31.245 

9657 

22 

0.345 

—0.430 

10 




0.230 

0 

25 

31.199 

9141 

23 

0.345 

—0.430 

10 




0.230 

0 

30 

31.283 

8843 

24 

0.345 

0.430 

15 




0.230 

0 

20 

32.064 

11202 

26 

0.345 

0.430 

20 




0.230 

0 

25 

32.025 

11231 

27 

0.345 

0.430 

25 




0.230 

0 

30 

31.868 

11062 

28 

0.345 

—0.430 

15 




0.230 

0 

20 

31.441 

10126 

29 

0.345 

—0.430 

20 




0.230 

0 

25 

31.510 

10141 

30 

0.345 

—0.430 

25 




0.230 

0 

30 

31.575 

10335 

32 

0.345 

0.430 

10 




0.345 

—0.430 

15 




0.230 

0 

30 

31.773 

9634 

33 

0.345 

—0.430 

10 




0.345 

0.430 

15 




0.230 

0 

30 

32.550 

11634 

34 

0.345 

0.430 

10 




0.345 

—0.430 

20 




0.230 

0 

30 

32.331 

10630 

35 

0.345 

—0.430 

10 




0.345 

0.430 

20 




0.230 

0 

30 

31.847 

10515 

36 

0.345 

0.430 

10 




0.345 

—0.430 

25 




0.230 

0 

30 

32.881 

11692 

37 

0.345 

—0.430 

10 




0.345 

0.430 

25 




0.230 

0 

30 

31.383 

9457 

38 

0.345 

0.430 

10 




0.345 

—0.430 

15 




0.345 

0.430 

20 




0.345 

—0.430 

25 




0.230 

0 

30 

32.194 

10650 

39 

0.345 

—0.430 

10 




0.345 

0.430 

15 




0.345 

—0.430 

20 




0.345 

0.430 

25 




0.230 

0 

30 

31.941 

10515 

40 

0.345 

0.430 

10 




0.230 

0 

15 




0.345 

0.430 

20 




0.230 

0 

25 

32.484 

11657 

41 

0.345 

—0.430 

10 




0.230 

0 

15 




0.345 

—0.430 

20 




0.230 

0 

25 

31.312 

9676 


% 


CONFIDENTIAL j 


APPENDIX 


227 


PRELIMINARY INDEX OF DIFFERENTIAL ANALYZER SOLUTIONS 
FOR ROC TRAJECTORIES 


This index records the data from differential 
analyzer trajectories for the Roc guided missile 
(00-1000-V) with range-control only. The same 
differential equations were used as for the Azon 
and Razon bombs. 

The value used for the control area A was 
t) ft^; for M, 1,700 pounds. The density function 
used was 

p= 0.959p,e-^-^^x^^'^^ 

where po = 0.002378 slug/ft^ is air density at 
sea level. The time of application of control is U. 
Where no control was applied this item is left 
blank. The indicated control continues until a 
new control at a new value of ti is applied, or 
until impact if no change in control is listed. 
Time of flight and range at impact are given by 
if and x(tf). The maximum value for the bomb 
velocity is given in miles per hour, and the trail 
angle in mils. 


The value of the drag coefficient Cd depends 
on whether or not brakes are used. For full 
brakes 

Cd = 0.413 + 0.310 Ci, 

where Cl is zero for no control and ±0.65 for 
maximum sail or dive. 

For no brakes 

= 0.122 + 0.310 C|. 

In some runs fractional amounts of brakes were 
applied. If this fraction is K, then 

Cd = 0.122 + 0.291 K + 0.310 Cl . 

All runs here recorded are made for an initial 
altitude of 15,000 feet, and initial velocity of 250 
miles per hour. Runs will be obtained later for 
different altitudes and velocities. 


RDA No. 119 Edition No. 5. Initial Altitude 15,000 feet. 
Initial Velocity 250 mph. 

00-1000-V Roc 


D O 

Brakes 

Control 

O 

Cl 

O 

o 

OQ 

? 

xn 

xUf) 

(feet) 

Max Roc 

Velocity 

(mph) 

Trail 

1 (mils) II 

II 

Brakes 

Control 

O 

Q 

o 

s 

t,(sec) 

1 

H w 

Max Roc 

Velocity 

(mph) 

Trail 

(mils) 

1 

Full 

None 

0 

0.413 

— 

36.332 

8744 

428 

302 

13 

None 

None 

0 

0.122 

— 





2 

Full 

None 

0 

0.413 







None 

75% Sail 

0.488 

0.196 

8 






Full 

Full Sail 

0.650 

0.543 

8 

51.600 

18152 

348 

52 


None 

75% Dive 

—0.488 

0.196 

18 

34.311 

8703 

544 

258 











14 

None 

None 

0 

0.122 







3 

Full 

None 

0 

0.413 

— 






None 

75% Sail 

0.488 

0.196 

8 






Full 

Full Dive 

—0.650 

0.543 

8 

37.774 

1519 

389 

701 


None 

75% Dive 

—0.488 

0.196 

16.75 

33.942 

8044 

545 

303 

4 

Full 

None 

0 

0.413 

— 





15 

Full 

None 

0 

0.413 

_ 






FuU 

75% Sail 

0.488 

0.487 

8 






Full 

75% Sail 

0.488 

0.487 

8 






Full 

75% Dive 

—0.488 

0.487 

22 

39.224 

8440 

402 

384 


Full 

75% Dive 

—0.488 

0.487 

18.5 

38.390 

7009 

355 

448 

5 

Full 

None 

0 

0.413 

— 





• 16 

Full 

None 

0 

0.413 

_ 






Full 

75% Sail 

0.488 

0.487 

8 






Full 

75% Sail 

0.488 

0.487 

8 






Full 

75% Dive 

0.488 

0.487 

23 

39.465 

8860 

402 

391 


Full 

75% Dive 

—0.488 

0.487 

17.75 

38.299 

6713 

406 

463 

6B 

None 

None 

0 

0.122 

— 

32.306 

10385 

597 

100 

18 

None 

None 

0 

0.122 







7 

None 

None 

0 

0.122 

— 






None 

75% Sail 

0.488 

0.196 

8 






None 

Full Sail 

0.650 

0.252 

8 

71.095 

33523 

383 

—470 


None 

75% Dive 

—0.488 

0.196 

16.75 





8 

None 

None 

0 

0.122 

— 






None 

None 

0 

0.122 

25 

33.673 

9725 

582 

176 


None 

Full Dive 

—0.650 

0.252 

8 

33.160 

1918 

502 

610 

19 

Full 

Full Sail 

0.650 

0.543 

0 





9 

None 

None 

0 

0.122 

— 






Full 

Full Dive 

—0.650 

0.543 

30 

45.542 

11090 

392 

364 


None 

75% Sail 

0.488 

0.196 

8 





20 

Full 

Full Sail 

0.650 

0.543 

0 






None 

75% Dive 

—0.488 

0.196 

20.5 

35.124 

10072 

544 

188 


Full 

Full Dive 

—0.650 

0.543 

24 

43.719 

8212 

383 

489 

10 

None 

None 

0 

0.122 


















None 

75% Sail 

0.488 

0.196 

8 





21 

Full 

Full Sail 

0.650 

0.543 

0 






None 

75% Dive 

—0.488 

0.196 

21 

35.285 

10377 

542 

172 


Full 

Full Dive 

—0.650 

0.543 

25 

44.000 

8692 

382 

469 

11 

Full 

None 

0 

0.413 







22 

None 

Full Sail 

0.650 

0.252 

0 






Full 

75% Dive 

—0.488 

0.487 

8 

35.582 

3998 

411 

553 


None 

75% Dive 

—0.488 

0.196 

20 

38.349 

9723 

538 

287 

12 

None 

None 

0 

0.122 

— 





23 

None 

Full Sail 

0.650 

0.252 

0 






None 

75% Dive 

—0.488 

0.196 

8 

31.626 

4183 

547 

459 


None 

75% Dive 

—0.488 

0.196 

21 

38.771 

10254 

537 

263 


■CONFimNTIALy 


228 


APPENDIX 


RDA No. 119 Edition No. 6. Initial Altitude 15,000 feet. 
Initial Velocity 250 mph. 

00-1000-V Roc 


Run 

No. 

Brakes 

Control 

►3 

<5 

o 

u 

<D 

'♦X' 

(sec) 

X(tf) 

(feet) 

Max Roc 

Velocity 

(mph) 

Trail 

(mils) 

2 

75% 

None 

0 

0.341 



35.345 

9109 

461 

256 

3 

75% 

None 

0 

0.341 

— 






75% 

75% Dive 

— 0.488 

0.415 

8 

35.039 

3599 

432 

563 

4 

25% 

None 

0 

0.196 

— 

33.308 

9929 

542 

154 

13 

25% 

None 

0 

0.196 

— 






25% 

75% Sail 

0.488 

0.270 

8 






Full 

75% Dive 

—0.488 

0.487 

19 

37.604 

8532 

411 

343 

14 

25% 

None 

0 

0.196 

— 






25% 

75% Sail 

0.488 

0.270 

8 






Full 

75% Dive 

—0.488 

0.487 

22 

38.216 

10084 

411 

261 

15 

25% 

None 

0 . 

0.196 

— 






25% 

75% Sail 

0.488 

0.270 

8 






Full 

75% Dive 

—0.488 

0.487 

16 

37.067 

7067 

410 

418 


Run 

No. 

Brakes 

Control 

>3 

o 

Cl 

O 

o 

<D 

CQ 

H 

<v 

CO 

X(tf) 

(feet) 

Max Roc 

Velocity 

(mph) 

Trail 

(mils) i 

16 25% 

75% Sail 

0.488 

0.270 

— 




Full 

75% Dive 

—0.488 

0.487 

19 

39.594 

8397 409 

395 

17 25% 

None 

0 

0.196 

— 




25% 

75% Sail 

0.488 

0.270 

8 




Full 

83.5% Dive 

—0.543 

0.504 

19 

37.741 

8148 407 

370 

18 25% 

None 

0 

0.196 

— 




25% 

50% SaU 

0.325 

0.229 

8 




Full 

75% Dive 

—0.488 

0.487 

19 

36.564 

8024 416 

374 

19 25% 

None 

0 

0.196 

— 




25% 

75% Sail 

0.488 

0.270 

8 




Full 

50% Dive 

—0.325 

0.446 

20 

37.676 

10135 422 

245 


( 

% 



NFIDENTIA 


APPENDIX 


229 


SUPPLEMENTARY INDEX OF DIFFERENTIAL ANALYZER SOLUTIONS 
FOR ROC TRAJECTORIES 


This index, like the preceding one, is of data 
on differential analyzer trajectories for the Roc 
guided missile (Douglas symbol: 00-1000-V) 
with range-only control, using the same con- 
stants. 

Control area: A = 9 sq ft 
Mass: M = 1,700 lb 
Density: p = 0.959poe “ 

where po = 0.002378 slug/ft^ is taken as air 
density at sea level. 

As before U denotes the time of application of 
control, this item being left blank in the case of 
free fall. The amount of control is indicated as a 
certain per cent of the total available ; it is con- 
tinued until a new control is applied at a new 
value of ti, or until impact. The amount of con- 
trol is also given in terms of the value of the lift 
coefficient Cl, where this quantity is positive for 
sail, negative for dive. 

The runs of RDA No. 130, Editions No. 1 
and 2 given in this index differ from all previous 
trajectories in that any changes of control are 
applied continuously by the analyzer, the rate of 
change being determined by the time, 1.7 
seconds, during which the control surface passes 
from the neutral position of no control to that 
of maximum control. This is, when sail is first 
applied at = 8 seconds. Cl is given by 

up until the instant when Cl reaches the specified 
value, after which it is held constant until a new 
time ti, at which time a challenge is initiated in a. 
similar way. 

Cd is also varied continuously with Cl accord- 
ing to the formula 

Ci>= 0.209 + 0.310 Cl. 

In all the runs of this index 30 per cent of the 
brakes were applied, corresponding to a value 
of Cd of 0.209, when there is no control. 

As before tf is the time-of-flight in seconds, 
X (tf) the range-at-impact in feet. Trail angle at 
impact is given in mils, using as the definition 
of a mil 6,400 mils = 360 degrees. 


RDA No. 130 Editions No. 1 and 2 00-1000-V Roc 


Kun 

No. 

Initial 

Velocity 

^ "o 



3 

tf (sec) 

X (tf) 

(feet) 

Max. Roc 

Velocity 

(mph) 

Trail 

(mils) 




Initial Altitude 5,000 feet 




7 

200 

None 

0 

0.209 

— 

18.417 

4827 

378 

116.7 

4 

250 

None 

0 

0.209 

— 

18.507 

5961 

391 

166.6 

8 

300 

None 

0 

0.209 

— 

18.601 

7061 

404 

225.0 




Initial Altitude 12,500 feet 




44 

150 

None 

0 

0.209 

— 

30.034 

5606 

500 

81.4 

55 

150 

60% 

0.390 

0.256 

8 







60% 

—0.390 

0.256 

15.4 

30.687 

4667 

480 

168.3 

30 

200 

None 

0 

0.209 

— 

30.168 

7371 

505 

119.8 

56 

200 

80% 

0.520 

0.293 

8 







80% 

—0.520 

0.293 

15.4 

31.467 

6159 

467 

245.3 

29 

250 

None 

0 

0.209 

— 

30.311 

9085 

508 

164.0 

35 

250 

75% 

0.488 

0.283 

8 







75% 

—0.488 

0.283 

15 

31.488 

7747 

475 

300.5 

38 

250 

75% 

0.488 

0.283 

8 







75% 

—0.488 

0.283 

12.5 

30.779 

6706 

477 

357.7 

48 

250 

100% 

0.650 

0.340 

8 







100% 

—0.650 

0.340 

15.4 

32.576 

7541 

449 

345.0 

52 

250 

95% 

0.618 

0.327 

8 







95% 

—0.618 

0.327 

15.4 

32.351 

7613 

455 

333.7 

31 

300 

None 

0 

0.209 

— 

30.468 

10734 

513 

214.5 




Initial Altitude 15,000 feet 




43 

150 

None 

0 

0.209 

— 

33.211 

6096 

528 

82.0 

42 

150 

25% 

0.163 

0.217 

8 







25% 

—0.163 

0.217 

17 

33.349 

5514 

525 

123.1 

47 

150 

50% 

0.325 

0.242 

8 







50% 

—0.325 

0.242 

17 

33.874 

4997 

511 

165.3 

53 

150 

45% 

0.293 

0.236 

8 







45% 

—0.293 

0.236 

17 

33.740 

5097 

515 

156.7 

5 

200 

None 

0 

0.209 

— 

33.362 

8011 

531 

119.9 

13 

200 

75% 

0.488 

0.283 

8 







75% 

—0.488 

0.283 

20 

35.661 

7883 

490 

173.2 

15 

200 

75% 

0.488 

0.283 

8 







75% 

—0.488 

0.283 

21 

35.909 

8393 

489 

144.3 

18 

200 

50% 

0.325 

0.242 

8 







50% 

—0.325 

0.242 

20 

34.563 

7987 

513 

145.0 

19 

200 

71% 

0.462 

0.276 

8 







71% 

—0.462 

0.276 

17 

34.827 

6471 

496 

249.2 

20 

200 

71% 

0.462 

0.276 

8 







71% 

—0.462 

0.276 

17.2 

34.856 

6568 

496 

243.5 

22 

200 

71% 

0.462 

0.276 

8 







71% 

—0.462 

0.276 

20.6 

35.606 

8201 

494 

151.2 

26 

200 

71% 

0.462 

0.276 

8 







71% 

—0.462 

0.276 

22.4 

36.061 

9084 

492 

101.0 

33 

200 

65% 

0.423 

0.264 

8 







65% 

—0.423 

0.264 

20.6 

35.311 

8213 

499 

144.6 

41 

200 

50% 

0.325 

0.242 

8 







50% 

—0.325 

0.242 

17 

34.059 

6914 

514 

206.1 

46 

200 

60% 

0.390 

0.256 

8 







60% 

—0.390 

0.256 

17 

34.428 

6739 

506 

224.4 

50 

200 

60% 

0.390 

0.256 

8 







40% 

—0.260 

0.230 

17 

34.318 

7634 

719 

163.7 

60 

200 

60% 

0.390 

0.256 

8 







80% 

—0.520 

0.293 

17 

34.779 

5860 

486 

286.9 




ONFIDENTIAL 


f 


230 


APPENDIX 


RDA No. 130 Editions No. 1 and 2 {Continued) 


Run 

No. 

Initial 

Velocity 

(mph) 

Control 

O 

CJ 

O 

O 

0? 

w 

tf (sec) 

X (tf) 

(feet) 

Max Roc 

Velocity 

(mph) 

Trail 

(mils) 

Run 

No. 

Initial 

Velocity 

(mph) 

Control 

O 

Q 

O 

O 

O 

w 

o 

o 

w 

X(tf) 

(feet) 

Max Roc 

Velocity 

(mph) 

Trail 

(mils) 

64 

225 

None 

0 

0.209 

— 

33.431 

8927 

533 

142.0 

61 

150 

40% 

0.260 

0.230 

8 





62 

225 

67% 

0.436 

0.268 

8 







40% 

—0.260 

0.230 

18.5 

36.750 

5376 

539 

156.4 



67% 

—0.436 

0.268 

17 

34.816 

7463 

500 

267.1 

27 

200 

None 

0 

0.209 

— 

36.342 

8602 

554 

119.1 

63 

225 

67.5% 

0.439 

0.269 

8 





58 

200 

50% 

0.325 

0.242 

8 







67.5% 

—0.439 

0.269 

17 

34.831 

7455 

500 

268.0 



50% 

—0.325 

0.242 

18.5 

37.292 

7162 

533 

216.5 

2 

250 

None 

0 

0.209 



33.523 

9870 

534 

163.1 





















28 

250 

None 

0 

0.209 

— 

36.503 

10603 

556 

160.6 

3 

250 

75% 

0.488 

0.283 

8 

















75% 

—0.488 

0.283 

20 

36.206 

9732 

492 

236.3 

34 

250 

75% 

0.488 

0.283 

8 

















75% 

—0.488 

0.283 

19 

39.046 

8650 

507 

319.0 

11 

250 

75% 

—0.488 

0.283 

8 

















83.5% 

—0.543 

0.300 

21 

36.600 

9966 

485 

230.6 

39 

250 

75.5% 

0.491 

0.284 

8 





12B 

250 

75% 

0.488 

0.283 

8 







75% 

—0.488 

0.283 

21.5 

39.726 

10092 

507 

255.0 



75% 

—0.488 

0.283 

17 

35.344 

8205 

494 

312.7 

49 

250 

75% 

0.488 

0.283 

8 





40 

250 

75.5% 

0.491 

0.284 

8 







75% 

—0.488 

0.283 

18.5 

38.903 

8345 

507 

332.3 



75% 

—0.488 

0.283 

18.5 

35.752 

8974 

493 

274.0 

51 

250 

50% 

0.325 

0.242 

8 





6 

300 

None 

0 

0.209 

— 

33.683 

11672 

538 

210.7 



50% 

—0.325 

0.242 

18.5 

37.566 

9152 

536 

263.0 

21 

300 

79% 

0.514 

0.291 

8 





54 

250 

65% 

0.423 

0.264 

8 







79% 

—0.514 

0.291 

17 

35.909 

9875 

492 

383.2 



65% 

—0.423 

0.264 

18.5 

38.290 

8692 

520 

302.1 

23 

300 

79% 

0.514 

0.291 

8 





57 

250 

63% 

0.410 

0.261 

8 







79% 

—0.514 

0.291 

14.6 

35.065 

8630 

487 

433.5 



63% 

—0.410 

0.261 

18.5 

38.179 

8757 

523 

296.4 

24 

300 

79% 

0.514 

0.291 

8 





32 

300 

None 

0 

0.209 

_ 

36.675 

12539 

559 

206.5 



79% 

—0.514 

0.291 

13.4 

34.661 

8032 

494 

456.9 











25 

300 

79% 

0.514 

0.291 

8 







Initial Altitude 30,000 feet 



• 


79% 

—0.514 

0.291 

12 

34.194 

7347 

494 

483.0 











36A 

300 

100% 

—0.650 

0.340 

8 





9 

250 

None 

0 

0.209 

— 

49.288 

13704 

636 

147.3 



100% 

—0.650 

0.340 

13.5 

35.896 

7155 

462 

532.2 

14 

250 

75% 

0.488 

0.283 

8 





37 

300 

85% 

0.553 

0.304 

8 







75% 

—0.488 

0.283 

28 

55.973 

9616 

573 

355.2 



85% 

—0.553 

0.304 

14 

35.156 

8093 

485 

465.5 

16 

250 

75% 

0.488 

0.283 

8 







Initial Altitude 17,500 feet 






75% 

—0.488 

0.283 

31 

56.382 

12522 

570 

270.2 

45 

150 

None 

0 

0.209 

_ 

36.194 

6543 

552 

82.4 

17 

250 

50% 

0.325 

0.242 

8 

















50% 

—0.325 

0.242 

31 

52.805 

13831 

604 

185.7 

59 

150 

38% 

0.247 

0.228 

8 

















38% 

—0.247 

0.228 

18.5 

36.416 

5552 

550 

142.3 

10 

300 

None 

0 

0.209 

— 

49.481 

16241 

637 

185.7 



ENTIA' 


GLOSSARY 


AIBR. Acceleration-integrator bombing release. A name for 
toss-bombing component of Bureau of Standards origin. 

.\ZOX. Stands for AZimuth OXly. A guided bomb for linear 
ground targets. Radio-controlled and flare-observed. 

BARB. British-type angular rate bombsight. An American 
name for certain instruments based on the British-invented 
principle of absolute angular-rate bombing criteria for 
low altitudes. 

Bug. An apocryphal name for target used in bombing trainers. 
Crawls on the floor. Certain species crawl in circles, or are 
unpredictable to the trainee. 

CART. Constant-angular-rate turntable. Testing apparatus 
for angular rate meters. Typically, suspended torsion 
pendula for accurate studies. 

CARP. Chronometric, automatic, ROC (or RAZOX) predictor. 
Alternatively, CRAB actually reaches perfection. A sight 
for guided bombs, involving a program leading to terminal 
collinearity over an interval. 

CLIP. Computation of lead with an inertia-pendulum. A dis- 
carded, but often recalled, project of questionable origin. 

CRAB. Chronometric range-anticipator bombsight. Other 
names have also been applied and are appropriate. A sight 
for aiding the guider of RAZOX in range, principally, in 
which the terminal point is predicted in terms of the time 
of flight. Attaches to the bombsight Mark 15. 

DBS. Dive bombsight. A sight develojjed by M. Alkali and 
Specialties, Inc. for the Xavy. Toss principle with freed gyro. 

DOVE. Origin unknown to UTiter. A high-angle guided or 
homing bomb with “spoilers” or “deflectors” in front for 
stoering. Polaroid, Xavy project; Division 5 cognizance. 

GCB. Ground-controlled bombing. As with RAZOX; ground 
stations steer bomb to target on known bearings. 

GOAD. Giving only angular depression. Local name for rudi- 
mentary “triangular-solution” bombsights (visual). 


GRASP. Gyroscopic, rocketeers, automatic, sighting predictor; 
or gyroscopic RASP. A rocket sight and computer for 
attachment to the gyro gunsight, as Mark 23. 

JAG. Just another gadget. A time-of-flight corrector, for use 
with guided bombs and CRAB. 

MIMO. jMiniature IMage Orthodon. Small television camera 
and transmitter for ROC. ' 

Orthopentax. Linkage having five perpendicular axes, of 
many and diverse applications. 

PACT. Pilot’s automatically computing toss bombsight. A 
linkage computer, with (pneumatic) integrator of incre- 
mental acceleration, and automatic release. 

PARS. Pilot’s automatic rocket sight. A miniature computer 
as aiming control for forward-fired rockets. 

Preset. Xame given to computers for bombers or bombar- 
diers. For auxiliary function to bombsight Mark 15, giving 
rate-knob adjustment, etc., in advance. 

PUSS. Pilot’s universal sighting systems. Computer for guns, 
rockets, and bombs, to be employed in fighter airplanes, etc. 

RASP. Rocketeer’s automatic sighting predictor. An early 
project which resulted in an experimental pilot’s rocket sight. 

RAZOX. Stands ostensibly for RAnge and AZimuth OXly. 
Very misleading. Should have been AZAR, for AZimuth 
And Range, for example. Two-coordinate AZOX, intended 
for point targets. 

ROC. Douglas high-angle guided bomb. Xamed for the roc 
or rokh, a giant bird of Arabian mythology. 

Sniffer. Low-altitude blind bombsight, invohdng f-m radar. 
Employs range, range rate, and altitude in automatic 
computation of release condition. 

VASS. Vosseller antisubmarine sight. Hand-held bombsight 
based on Vosseller’s method of extrapolation. Chronometric. 

VERB. Prehistoric name used for RASP. Rocket bombsight, 
preceded by two words, which are now unknown; perhaps, 
very exceptional. 


231 





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BIBLIOGRAPHY 


Numbers such as Div. 7-1 12.1 1-Ml indicate that the document listed has been microfilmed and that its title appears 
in the microfilm index printed in a separate volume. For access to the index volume and to the microfilm, consult 
the Army or Navy agency listed on the reverse of the half-title page. 


1 . 


2 . 


3. 


4. 


5. 


6 . 


7. 


8 . 


PART I 


Chapter 1 


Chapter 2® 


Corrections Necessary in Aiming a Machine Gun, Mounted 
on an Airplane, at a Moving Target, J. R. Moore, K8064695, 
General Electric Company, June 1941. 

A good exercise in vectorial methods, and some fundamental ballistics 
for aerial gunnery, by one of the most active workers in this field. 

Gyroscopic Lead Computing Sights, Report to the Ser- 
vices 13, NDRC Section D-2, August 1941. 

Div. 7-112.11-Ml 

An exposition, on fundamental grounds, of the technique of lead 
computing, principally with regard to a single “disturbed” gyro of 
the eddy current dome variety. Derivations of the familiar formulas 
are included, as also is a compete physical interpretation of the 
theoretical steps. 

An Introduction to the Analytical Principles of Lead 
Computing Sights, Saunders MacLane, OEMsr-1007, 
AMP Memo 55.1, AMG-Columbia, March 1944. 

AMP-503.6-M21 

Mathematically rigorous and accomplished treatment of the classical 
lead computing dynamics. Fundamental concepts are explained and 
developed to show the current stage of the theory. A glossary of 
notation (with translations) and a good bibliography are included. 

Pursuit Courses, Walter Leighton, OEMsr-1007, AMP 
Memo 57.4, AMG-Columbia, Mar. 29, 1944. 

AMP-503.7-M1 

A study in detail of such courses, in the air and with respect to the 
target, with thoroughgoing rigor. Both pure pursuit and that with 
lead are treated, although “mushing” is not considered. Tables are 
included for several standard approaches. 

The Extrapolation, Interpolation and Smoothing of Sta- 
tionary Time Series, Norbert Wiener, OSRD 370, Re- 
search Project DIC-6037, Report to the Services 19, 
NDRC Section D-2, MIT, Feb. 1, 1942. Div. 7-313.1-M2 

An extension of some Russian work, using the methods of communi- 
cations engineering, statistical theory, and Fourier analysis. The 
author’s earlier work is relevant hereto. Not so difficult to react as 
is commonly supposed. 

Statistical Method of Prediction in Fire Control, Norbert 
Wiener and Weaver, NDCrc-83, Report to the Services 
59, Research Project 6, Dec. 1, 1942. Div. 7-112.2-M2 

Contains a discussion of some of the results of reference 5 above, 
and of their probable importance in the prediction of straight flight 
and of flight which is accelerated in various ways. Comparisons 
among known methods of prediction are included, together with- 
certain historical material. 

An Exposition of Wiener’s Theory of Prediction, N. 
Levinson, OEMsr-1384, AMP Note 20, AMG-Harvard, 
June 1945. AMP-13-M21 

Develops the autocorrelation function more gradually, showing that 
the linear prediction problem reduces to that of the solution of an 
integral equation. Practical and mathematical difficulties in applica- 
tion are discussed, and errors in prediction are interpreted in 
mathematical form. 

Collision Courses by Method of Overcorrecting Changes in 
True Bearing, (Capt.) V. A. Kimberly, USN, Letter to 
Chief BuOrd from Special Board on Naval Ordnance, 
September 1927. 

This letter gives an elementary explanation, in terms of surface 
vessels, of the method named, and shows how and why the method 
leads to a straight interception as the range closes up. There are not 
many such explanations available in the literature. 


1. Electrical Simulation of the Human Operator in Tracking 
Mechanisms as an Aid in the Study of Sight Dynamics, 
R. H. Randall and F. A. Russell, OEMsr-1237, TR 
T-13, NDRC-Section 7.2, Columbia University Division 
of War Research, June 21, 1945. 

A report on work originally urged by the present writer. The attempt 
is described to employ a proposed representation of the operator </> 
in lieu of the real thing for laboratory tracking experiments. 

2. Investigation of the Operator’s Response in Manual Control 
of a Power Driven Gun, A. Tustin, C. S. Memorandum 
169 (British). 

A review of this memorandum is given in the report last men- 
tioned. 

3. Tracking Aircraft with Heavy Turrets, Merz and Mc- 
Lellan, British Liaison Code WA-1711-1. 

Sets up and studies the hystero-differential equations which result 
for the ensemble when a direct time delay is attributed to the 
human operator. Conditions for stability and learning are considered 
somewhat qualitatively. 

4. Some Characteristics of Human Operators in Control 
Systems, K. J. W. Craik (Cambridge University), Min- 
istry of Supply Informal Panel on Servomechanisms, 
British Liaison Code WA-1641-6, Great Britain, Feb. 4, 
1944. 

Apparatus and techniques are described whereby the human operator 
w'as studied when performing with direct tracking. Curves of pursuit 
agree substantially with those obtained in our laboratories. The 
effects of the excellence of the display and other psychological aspects 
of the problem are disciissed. Also, the transient and harmonic 
methods of investigation are compared. 

5. The Conduction of the Nervous Impulse, Keith Lucas, 
Longmans Green and Company, revised, 1917. 

Contains evidence that nerve conduction, in the large, is a linea- 
phenomenon, the time relations therein being apparently inder 
pendent of the strength of stimulus. (This is contrary to the popular 
conception.) Reflex phenomena are discussed as being a local affair 
connected with the nerves themselves. 

6. The Mechanism of Nervous Action, E. D. Adrian, 
Eldridge Reeves Johnson Foundation, 1931 Lectures, 


^ The reader’s attention is called to the related bibliography included 
in the list for Chapter 1. The writings of H. Whitney on tracking, which 
have been promulgated by AMG-Columbia of the Applied Mathematics 
Panel, should also be referred to. Whitney’s views, which are arrived at 
through a minimum of quantitative experiment and a maximum of per- 
sonal intuition, are nevertheless worthy of attention. Although most of 
his work has been in connection with turrets, see also his AMG-Columbia 
Working Paper 329, of Dec. 13, 1944, Notes on the Tracking Problem for 
Fighter Planes, which advances explanations for some of the anomalous 
results observed in this kind of tracking. For quantitative material, with 
extensive collation and analysis, relating to the man-machine interactions 
with standard types of tracking with lead-computing sights, see the rich 
body of literature which has accumulated under the program sponsored 
by Section 7.2 at The Franklin Institute. This work will be reported 
upon fully by S. H. Caldwell, J. B. Russell, and H. C. Wolfe of that 
section. For the contractor, the psychologists Preston and Irwin, who 
have been proteges of S.W. Fernberger at the University of Pennsylvania, 
were in control of the experimental and analytic procedures involved, 
and their reports are models of exhaustive disclosure and of zealous 
adherence to the dictates of the data. 



233 


234 


BIBLIOGRAPHY 


Press of the University of Pennsylvania, 1932. 

In this book evidence is given, and is referred to there as proof, 
that the workings of the nervous system are not beyond mechanical 
description. 

7. Pursuitmeiers: Alcohol and Human Efficiency, W. R. 
Miles, Carnegie Institute Publication. 

Apparatus involves complex harmonic generation using wattmeter, 
error indicator, and manually operated slide-rheostat. Very modern 
in spirit and objective. Continuous records are shown. 

8. “A Pursuit Device for Obtaining both Quantitative and 
Qualitative Records,” R. M. Collier, Journal of Psy- 
chology, Vol. 2, 1936, pp. 295-300. 

Description of curve-drawing apparatus similar to that constructed 
at The Franklin Institute in the earliest work on the human tracking 
response. In contrast to the pursuitmeters of this reference and 
reference 7, most such equipment is of the discontinuous, or aver- 
aging, variety. 

Chapter 3 

1. Further Application of the Strain Gauge to Gyroscopic 
Measurements of Angular Rates, J. D. Eisler, U. C. S. 
Dilks, and W. W. Felton, Report 152, Franklin Institu- 
tute, Nov. 9, 1943. 

Title is self-explanatory. The principal application in mind was to 
lead-computing sights. Methods and apparatus are described for 
eompensation required for gyro speed changes, temperature, etc. 
The noise problem is explained, together with its possible solution. 
Circuits and photographs are shown. 

2. Symmetrically Constrained Gyros as Angular Rate Indi- 
cators, M. Golomb, Report 218, Franklin Institute, 
July 27, 1945. 

A theoretical treatment of the dynamics involved in the gyro 
suspensions proposed for the simultaneous measurement of angular 
rate about two axes with a single gyro. Several types of constraint 
are considered, and the stability conditions expressed. The effects 
are described of static friction in the gimbals. 

3. Servo-Controlled Gyroscope, U. C. S. Dilks and M. 
Golomb, Report 238, Franklin Institute, Oct. 7, 1945. 

Theory and construction of the two-dimensional, electric captive 
gyro under development for PUSS. Its effectiveness, in speed and 
accuracy for large and small absolute angular rates, is discussed along 
with its limitations. Circuits are given, as well as methods of testing, 
and the numerical data are included on the basic gyro component 
involved. 

Chapter 4*^ 

1. Control Circuits for Radio Controlled Units, J. R. Ragaz- 
zini and L. Julie, Diary of Columbia Project, OEMsr- 
1237, Dec. 8, 1943. 

Contains a brief exposition of the simulative philosophy as applied 
to control problems. Electronic details are omitted but are implicit. 
Practical exercises, for sight-simulation, guided bombs, etc., should 
be consulted for circuits. 

2. Diary Concerning a Conference on November 29 on Subject 
of Columbia Project, J. R. Ragazzini, OEMsr-1237, 
Dec. 14, 1945. 

Proposals for simulation of control deflections having boundary 
conditions, as under human operation. Use of feedback amplifiers, as 
integrators, etc., outlined, preparatory to the simulative project on 
guided missiles. 

3. Simulation of PUSS Rocket Sight, J. R. Ragazzini, 
OEMsr-1237, NO-265, Report M-35, Columbia Univer- 


sity, June 11, 1945. 

Shows the then proposed PUSS formulas, and details for their 
simulation electronically. 

4. Aerodynamic Constants for a Simulated Airplane, F. A. 
Russell, OEMsr-1237, NO-265, Report M-38, Columbia 
University, June 13, 1945. 

Arrangement of degrees of freedom, and their connecting relations, 
for the simulative project. 

5. Axis Conversion, R. H. Randall, OEMsr-1237, Report 
M-36, Columbia University, June 21, 1945. 

Application of rigid-body dynamics to the problem of airplane 
simulation. Coordinate systems are worked out, after much deliber- 
ation, which appear manageable for incorporation in the electronic 
model components. 

6. Airplane Simulator {for Small Angles), F. A. Russell and 
R. H. Randall, OEMsr-1237, NO-265, Report M-32, 
Columbia University, June 21, 1945. 

Summary of the first working phase of the simulative development 
for PUSS. References to the aerodynamic literature are included, 
as are the schematic circuits employed in simulation. 

7. On the Study of Cyclic Dynamical Systems by Means of 
Equivalent Networks, L. Jafek, Cossor Industries, Aug. 
5, 1942. 


Chapter 5° 

1. Theory of Gyroscope Suspended in a GAP Linkage, M. 
Golomb, Memo to G. A. Philbrick, Franklin Institute, 
Dec. 14, 1944, 

An analysis of the orthopentax employed as a gyro suspension. Its 
possibility as forming a lead-computing system for PUSS was then 
being explored. Certain practical advantages were expected, but 
no practical application has yet been made. 


Chapter 6 

1. Torpedo Director, Mark 32, R. W. Pitman, OSRD 5079, 

OEMsr-330, NO-106, Report 172, Franklin Institute, 
Jan. 26, 1944. Div. 7-141-Ml 

Describes the final model of the torpedo director which resulted 
from Project NO-106. Foreword by A. L. Ruiz. Figures and re- 
writing by G. A. Philbrick. This document is in the form of an 
instruction manual, but is roughly definitive of the whole develop- 
ment prior to 1944. 

2. Torpedo Director, Model Number One, R. W. Pitman, 
R. K. Marshall, F. W. Schlesinger, and others, NO-106, 
Report 120, Franklin Institute, Aug. 15, 1942. 

Covers phases of work on this project during the first half-year of 
development. Describes vector theory and first mechanizations 
thereof. Discusses the problem of stabilization in azimuth. Appen- 
dices treat related problems, such as the optical ones connected 
with the pilot’s sight head. References are included to even earlier 
documents. 

® For documents on the computing linkages such as are being prepared 
for the PUSS project at The Franklin Institute, this contractor’s final 
report, not received at the present writing, should be consulted. It is now 
expected that this work is to be extended under Navy auspices, so that 
another future source of information will be Section ReSc of the Bureau 
of Ordnance. 

The final report of The Bristol Company under their contract (OEMsr-1387) 
with NDRC Section 7.2, may also be consulted, in connection particularly 
with manipulated linkage developed within the PUSS project. 

See also Radiation Laboratory (MIT) , and Librascope Corporation reports, 
for other computing linkages. 


^ See also Chapter 8. 


BIBLIOGRAPHY 


235 


3. The Electrical Solution for the Torpedo Director {NO-106), 
J. D. Eisler, Report 135, Franklin Institute. 

Describes the a-c vector embodiment of the same theory as in 
mechanical directors. Certain advantages in flexibility of installation 
were thus sought, and a technique was experimentally developed 
for further applications. Many circuits and photographs are shown. 

4. Stabilization of the Mark 31 Torpedo Director for Motor 
Torpedo Boats, J. D. Eisler, NO-134, Report 148, 
Franldin Institute, June 15, 1945. 

Mainly a servo development which derived stabilization for the 
target velocity, as set in this director, by means of the Flux-gate 
compass. Details of the construction. Test data are not included, 
but good operation was experienced in field tests at the MTBSTC 
at Mehnlle, Rhode Island. 

Chapter 7 

1. U.S. Navy Bombsight Mark 20, R. W. Pitman and others. 
Report 200, Franklin Institute, August 1943. 

Div. 7-122.2-IM2 

A descriptive manual of the theory and instrumental principles, 
and of the installation and maintenance of this bombsight. Detailed 
instructions for operation, with pictorial aids, are included. 

2. Auxiliary Ground Speed Computer, John A. Be van and 
others. Report 167, Franklin Institute, Dec. 12, 1943. 

Description of, with instructions for use of, a miniature mechanical 
computer for use with hand-held bombsights. Of wider applicability, 
however. 

3. Automatic Altitude Adjustment for Bombsight Mark 20, 
U. C. S. Dilks, OSRD 5080, OEMsr-330, NO-129, 
Report 161, Franklin Institute, Jan. 24, 1944. 

Div. 7-122.2-Ml 

Account of an experimental project wherein the altitude determined 
by the f-m radio altimeter is servoed into the bombsight continu- 
ously. Very small equipment resulted, attachable without inter- 
ference to a hand-held instrument. A d-c resistive feedback principle 
is applied. 

4. Bombsight V, Model 3, John A. Bevan, Report 168, 
Franklin Institute, Mar. 6, 1944. 

This is one of the many adaptations of the basic principle of the 
Mark 20, although without chronometric extrapolation. Each modi- 
fication led to diminishment in size and complexity. Very satisfactory 
results were obtained in flight tests at NAS Banana River. 

5. Bombsight VI, LTA, John A. Bevan, Report 178, 
Franklin Institute, Ma> 6, 1944. Div. 7-122.4-M2 

An adaptation of bombsight V, so-called, to the bombing problem 
of blimps. This sight became bombsight Mark 24 and enabled a 
surprising accuracy of dropping. 

6. Slant Range Computer, R. W. Pitman, Report 156, 

Franklin Institute, Nov. 5, 1943. Div. 7-123-Ml 

Description of a small, flat, manually operated computer, giving the 
slant range at which bomb release should occur, in horizontal flight 
at low altitude, in terms of altitude and closing speed. One-hand 
operation. Model submitted to BuAer. 

7. The Preset Computer Model 3, John A. Bevan, OSRD 

5088, OEMsr-330, NO-191, Report 189, Franklin Insti- 
tute, July 7, 1944. Div. 7-123-M2 

A mechanical computer, the final model of several developed, 
supplying preliminary information on how synchronizing run to the 
high-altitude bombsight operates. Inputs are manually applied, 
except azimuth stabilization, which is automatically provided. 

8. Report on the Strain Gauge BARB, J. D. Eisler, Report 
155, Franklin Institute, June 1943. 

Experimental angular-rate measurement from processing torque of 
a restrained gyro, strain gauges being applied to the restraining 
members. Also its tentative application to a low-altitude bombsight. 


9. Notes on Low Altitude Bombing, I — VII, G. A. Philbrick 
and R. M. Peters, Research Project 33, NDRC Section 
7.2, Franklin Institute, May 1943 — March 1944. 

Div. 7-122. 1-M3-9 

A series of studies, concerned principally with the theoretical 
evaluation of bombing errors, for the various known methods 
(including BARB), in terms of the several variables of the problem. 
An account of the BARB theory is included, with predictions, later 
upheld, of the comparative results obtainable. Offset bombing and 
glide bombing are considered by various methods. A “hybrid” 
BARB is shown to be substantially unworkable, so that no time was 
wasted on it. The writing of L. Goldberg, under the auspices of 
Section 7.3, should also be referred to in these connections. BARB 
eventually became bombsights IMark 23 and 27. These are, more 
precisely, BARB and SuperBARB. 

10. Gyroscopic Lead Computing Sights, Report to the Ser- 
vices 13, August 1941. Div. 7-122. 11-Ml 

Chapter 8 

1. Norden Bombsight Attachment for Guiding AZON f 
RAZON Bombs, John A. Bevan, OSRD 5740, OEMsr- 
330, AC-36, Report 194, Report to the Services 97, 
Franklin Institute, Oct. 10, 1944. Div. 7-122.4-Ml 

A description, briefly, of the theory and nature of the CRAB sight, 
with instructions for its installation, calibration, and employment 
operationally. Adapted by NDRC Division 5 to Preliminary Tech- 
nical Manual, CRAB, An Attachment to the Norden-Type Bombsight 
for Aid in Guiding Flare-Equipped Bombs, issued in June 1945. 

2. Notes on Calibration, Installation, and Operation of 
CARP, John A. Bevan, Report 199, Franklin Institute, 
Oct. 12, 1944. 

Descriptive material on CARP, with an appendix giving theory, 
especially of the artificial disk speed technique. Includes functional 
diagrams, circuits, and photographs. No clues as to why CARP 
ROC combination failed as a collinear flare-guiding system. For 
related matters on ROC, and the other projectiles and vehicle- 
controls, the reader is referred to the report of NDRC Division 5 
and its contractors, particularly Gulf Research and Development, 
and Douglas Aircraft. Note in particular the writings of W. B. 
Klemperer of the latter organization. 

3. Study of AZON Control and Regulation, L. Julie, OEMsr- 
1237, Report 7-1, Columbia University, May 10, 1944, 

Describing the initial simulative system whereby the dynamics of 
guiding were electronically reproduced in the laboratory. Records 
of the RDA No. 2 at MIT should be consulted for more precise 
data on trajectory shapes. 

4. Completion of Trainer Project, L. Julie, OEMsr-1237, 
Report M-23, Columbia University, Oct. 21, 1944. 

Exposition of the final experimental form of the universal guided- 
bomb simulator, for AZON, RAZON, and ROC. This device was 
later produced as a field trainer for guiders by Division 5 agencies. 
Circuits and alignment techniques are given. 

5. The AZON-RAZON Bombing Trainer, (Models X-1010 
and X-1020), NDRC Division 5, Aug. 15, 1945. 

Div. 5-233-Ml 

Based on writings and developments of Section 7.2, applied to guided 
bombing equipment. Attachment of electronic simulative equipment 
to Army A-6 and A-5 bombing trainers. Similar combinations, 
with the Navy 7A3 bombing trainer, were also carried out, in 
which a moving spot was projected on the synthetic landscape of 
the photographic trainer. 

6. Study of the Guiding Characteristics of the Television 
Bomb; including a Regulator for Guiding, L. Julie, 
OEMsr-1237, Report 7-14, Columbia University, June 
29, 1945. 

Employment of electronic simulative techniques to study the 
stability of a proposed control system for attaining interception 
under remote manual guiding, even with target motion in the air 


CONFTDEN 




236 


BIBLIOGRAPHY 


mass. Cooperation of simulator and human operator was exploited. 
Criticalness of control parameters was exhaustively studied and 
later fully corroborated elsewhere. 

Chapter 9 

1. Development of Rocket-Gun sights; Summary Report on 
NO-216, Eugene P. Cooper, Report 233, Franklin Insti- 
tute, Sept. 30, 1945. 

A review in some detail of the development on rocket sights at 
The Franklin Institute, with attention to historical sequence. An 
attempt is made to supply the logical steps which were followed. A 
brief account of the various field-testing programs is included, to- 
gether with connected references to other local reports on rocketry 
developments. This is essentially a final statement by the author, 
who was given considerable responsibility in this field. 

2. Sighting of Rocket Projectiles from Aircraft, C. W. Gil- 
bert, British Liaison Code, WA-3190-3, Gunnery Re- 
search Unit, RAF, Oct. 19, 1944. 

The tactics and aiming problem are developed, with a breakdown 
of the sighting problem in terms of the allowances for relative speed, 
trail (attack angle and skid), and gravity. Proposals are made for 
future development, and a general vector theory included. 

3. On the Use of the Lead-Computing Characteristics of the 
Mark 18 to Solve the Super-ElevationProblemfor Rocketry, 
Eugene P. Cooper, Memo to G. A. Philbrick, Franklin 
Institute, July 18, 1944. 

Cooper gives here the theory later embodied in the so-called British 
method of rocket aiming. Shows reasons for pessimism as to result. 
Note that this method ultimately generalized to PUSS. 

4. Gravity Drop Formulas for Airhorne Rockets, Harry 

Pollard, [OEMsr-1007], AMG-C Working Paper 347, 
AMG-Columbia, Jan. 4, 1945. AMP-603-M2 

Fitting of firing-table data to second-order space paths. See also 
various CIT rocket publications and firing tables. 

5. The RASP Rocket Sight— Model I, U. C. S. Dilks, E. C. 
Lewis, and others, OEMsr-330, NO-216, Report 188, 
Franklin Institute, Aug. 17, 1944. Div. 7-132-Ml 

A descriptive account of the RASP project in its primary phase. 
Includes the derivation of equations and their mechanization. A 
study of the theoretical accuracy is included, together with firing 
data from tests — with final reductions thereof, photographs, and 
circuits. Foreword by G. A. Philbrick of Section 7.2. 

6. The RASP Rocket Sight— Model III, U. C. S. Dilks, 

E. C. Lewis, and W. C. Sheppard, OSRD 5091, OEMsr- 
330, NO-265, Rejwrt 206, Franklin Institute, Feb. 1, 
1945 Div. 7-132-M2 

Comparisons with Model I are included throughout. The computa- 
tional technique is newly explained and an appendix is devoted to 
a more theoretical treatment of this technique, with general applica- 
tions. Many photographs are included, and circuits and servo 
components are described in detail. Analyses of test data, with 
statistical reduction, are included. A foreword is attached, prepared 
by G. A. Philbrick. 

7. [The] GRASP Sight for Forward Firing Aircraft Rockets, 

Model I, Eugene P. Cooper and Marjorie C. Cooper, 
OSRD 4991, OEMsr-330, NO-216, Report 211, Franklin 
Institute, Apr. 9, 1945. Div. 7-131-Ml 

The method is described, and a derivation is given of the equations 
to be employed. The details of the physical computation and of the 
instrumental components are elaborated upon, with a study of 
errors in firing. Very complete testing data are given. A foreword 
by G. A. Philbrick is attached. 

8. The GRASP Rocket Sight, Model II, Eugene P. Cooper 
and Marjorie C. Cooper, OSRD 6040, OEMsr-330, 
NO-216, Report 213, Franklin Institute, Sept. 30, 1945. 

Div. 7-131-M2 

Report 211 is here brought up to date for the newer model. (The 
Aircraft Rocket Sight Mark 2. For ARS Mark 3, the writings of 


H. Whitney, et al, of AMG-C should be referred to by the reader, 
where corresponding details of the jointly pursued PARS project 
are more fully covered.) In this report an exhaustive account of 
laboratory calibration is included, and, in the final edition, the 
results of firing tests at NOTS, Inyokern. A foreword by the present 
writer is attached. 

9. Measurement of Angle of Attack and Skid in Rocket Fire 
Problems, H. L. Garabedian, OEMsr-1379, AMG-N 
Working Paper 61 (revised), AMG-Northwestern, 
Sept. 12, 1945. AMP-502. 14-M 13 

A study of relations preparatory to a test program for skid. Camera 
techniques and coordinates. Bibliography of related writings. 

Chapter 10 

1. Analysis of Optical Systems for PUSS, I. M. Levitt, 
Report 241, Franklin Institute, Oct. 31, 1945. 

Containing a review of the problems and proposals in connection 
with the development of universal sight heads for the pilot. Collimat- 
ing lenses and mirror linkages are discussed, as are the possible 
modifications to this end of the interesting Fly’s Eye design. Illumi- 
nation problems are explored. Some tentative overall conclusions 
are arrived at The final report of the Bristol Company contract — 
with Section 7.2 — should also be consulted. 

2. Interim Report on PUSS, John A. Be van, Report 224, 
Franklin Institute, Aug. 24, 1945. 

A compilation of recent documents, arranged as seven independent 
appendices, and with an introduction on the current status of the 
project, including theory and design. Instrumental techniques are 
discussed, with a review of the input components, computers 
(including PACT for toss bombing), and .sight head. The electric 
and pneumatic versions of PUSS are described and compared. 

The appendices of this report, which are worthy bibliographic items 
in their own right, include memoranda and theoretical papers on 
gyro systems, computing dynamics (with competing theories), roll 
stabilization, etc., and were prepared chiefly by INI. Golomb and 
R. O. Yavne. 

3. Servo-Controlled Gyroscope, U. C. S, Dilks and M. 
Golomb, Report 238, Franklin Institute, Oct. 2, 1945. 

Theory and construction of the two-dimensional, electrically cap- 
tured gyro in development for PUSS. Effectiveness for small angular 
rates is discussed, with limitations included. Electronic circuits are 
given in detail, together with the electrical and other properties of 
the basic gyro unit which was adapted for this purpose. 

4. Development of Pilot-Operated Fire Control Equipment; 
Outline of the General Project, G. A. Philbrick, Ai)r. 25, 
1944. 

Preview of the PUSS Project. Aims and hopes for the development. 
Gives scope and instrumental specifications. Discusses aiming 
methods, including those without explicit range measurement. 
Proposed electronic tracking simulator for pilot-operated fire controls. 

5. Notes on Pneumatic PUSS; I, L. Charles Hutchinson, 

[OEMsr-1007], AMG-C Working Paper 461, AMG- 
Columbia, July 17, 1945. AMP-502. 1-M28 

Considers pneumatic embodiment of computing dynamics. Gives 
theory and brief experimental data. 

6. Notes on Pneumatic PUSS; II, L. Charles Hutchinson, 

[OEMsr-1007], AMG-C Working Paper 478, AMG- 
Columbia, Aug. 10, 1945. AMP-502. 1-M30 

Considers pneumatic component for the input giving rate of change 
of altitude. Circuits, theory, and numerical data. Includes non- 
linearities. 

7. PUSS, Target, Sight, Horizon Presentation, J. R. 
Ragazzini and R. H. Randall, OEMsr-1237, Report 
M-34, Columbia University, May 29, 1945. 

Simulative computational arrangements for pilot’s tracking simu- 
lator. Includes dynamics, coordinates to be employed, and the 
optical or oscilloscopic display. 


^XFIDENTIAI. 


BIBLIOGRAPHY 


237 


8. A Theory of Toss-Bombing, Harry Pollard, ()E]Msr-1007, 
AMP Report 146. IR, AMG-Columbia, September 1945. 

AMP-803.5-M12 

Principles of toss bombing on a revised basis. Measurables of the 
problem, including target motion. Mechanization of formulas, 
employing integral of normal acceleration. This is the definitive 
theory for PACT. 


9. The Azimuth Problem m Toss-Bombing, Harry Pollard, 
AMG-C Working Paper 495, AMG-Columbia, Sept. 18, 
1945. AMP-803.5-M13 

Shows an exact solution for the target motion in azimuth. The 
effect of roll and bank is included, and the appropriate sighting 
dynamics, for use with PUSS and PACT, are specified. 


PART II 

The following reports were all issued by The Franklin Institute under Contract OEMsr-330. 


1. Reflecting Sight for Torpedo Director, Report 330-1706- 

102, Apr. 17, 1942. 23. 

2. Torpedo Director N 0-106 — Tests on Sight Containing a 
Miniature Ship Model, Report 330-1706-103, May 6, 1942. 

3. Use of Radar Data in Torpedo Director N 0-106, Report 
330-1706-105, May 12, 1942. 

4. Altitude Speed Range Slide Rule for Simplified Torpedo 
Director NO-106, Report 330-1706-106, IMay 25, 1942. 

5. Torpedo Director NO-106: Principle and Operation of 
Experimental Director, Report 330-1706-107, May 26, 

1942. 

6. Torpedo Director NO-106 — Stabilizing Systems Using a 
Turn Gyro, Report 330-1706-108, June 1, 1942. 

7. Proposed Continuous Electrical Solution for Torpedo 
Director, Report 330-1706-109, July 25, 1942. 

8. A Stabilizing Method which Might be Applied to the 
Torpedo Director, Report 330-1706-110, July 25, 1942. 

9. Explicit Relation Between Present Range and Torpedo 
Run in the Torpedo Director NO-106, Report 330-1706- 
111, Aug. 6, 1942. 

10. A Two-Phase Stabilizer for Torpedo Director NO- 106, 

Report 330-1706-112, Aug. 15, 1942. 

11. An AC Current Controller for Stabilizing the Torpedo 
Director NO-106, Report 330-1706-113, Aug. 15, 1942. 

12. Reflecting Sight for Torpedo Director N 0-106, Report 
330-1706-114, Aug. 19, 1942. 

13. Torpedo Director NO-106 — Further Notes on Two-Man 
Operation, Report 330-1706-115, Aug. 20, 1942. 

14. Wind Effects Relative to Torpedo Director, Report 330- 
1706-116, Aug. 15, 1942. 

15. Effects of Interchange of Torpedo Run and Range on the 
Performance of Torpedo Director in Attacks on Bow of 
Target, Report 330-1706-117, Aug. 17, 1942. 

16. Torpedo Director N 0-106 Model Number One: Principles, 
Construction, Operation, Accuracy and Specifications, 

Report 330-1706-120, Aug. 15, 1942. 

17. Calibration of Torpedo Director for Use by Army Air 
Forces, Report 330-1706-121, Aug. 8, 1942. 

18. Torpedo Director NO-106, Flight Tests at Norfolk, Vir- 
ginia, Report 330-1706-123, Sept. 30, 1942. 

19. Preliminary Studies Leading to the Development of a 
Photoelectric Stabilizer for the NO-106 Torpedo Director, 

Report 330-1706-124, Oct. 15, 1942. 

20. A Photoelectric Stabilizer for the NO-106 Torpedo Director, 

Report 330-1706-125, Oct. 25, 1942. 

21. Conditions of Torpedo Running Time Affecting the Use 
of Torpedo Director N 0-106, Report 330-1706-128, 

Oct. 12, 1942. 

22. Tables and Graphs for Calibration of Torpedo Director 


NO-106, Report 330-1706-129, Oct. 10, 1942. 

Calibration Tests, Torpedo Director NO-106, Type ‘GT’, 
Report 330-1706-130, Oct. 26, 1942. 

Preliminary Study of Japanese Torpedo Director, Report 
330-1706-132, Nov. 10, 1942. 

Use of Torpedo Director — Errors in Lead Angle to be 
Expected from Errors in Ebti?natio7i of Fs, Target Speed, 
Report 330-1706-133, Dec. 7, 1942. 

Two-A utosyn Controller for Stabilizing the N 0-106 Tor- 
pedo Director, Report 330-1706-134, Dec. 21, 1942. 

The Electrical Solution of N 0-106 Torpedo Director, 
Report 330-1706-135, Jan. 12, 1943. 

Mark 32 Torpedo Director — Inaccuracies in Theory and 
Design, Report 330-1706-137, Mar. 14, 1943. 

General Solution of the Determination of Minimum Range, 
Time of Travel to This Point and Angle Between Course 
of M.T.B. and Minimum Range, Report 330-1706-140, 
Mar. 24, 1943. 

Adaptation of the General Electric Automatic Pilot Sydtem. 
to the Stabilization of the N 0-106 Torpedo Director,, 
Report 330-1706-142, Apr. 19, 1943. 

Use of a Rule-of-Thumb Method of Torpedo Direction,, 
Report 330-1706-145, May 4, 1943. 

M.T.B. Director: Preliminary Study of Applicability of 
Radar Data to Use of. Report 330-1706-146, May 1, 1943. 
Stabilization of Mark 31 Torpedo Director for M.T.B., 
Report 330-1706-148, June 15, 1943. 

F ield Tests of Stabilized Mark 31 Torpedo Director NO-134, 
Report 330-1706-149, June 16, 1943. 

Helmsman Direction Indicator for M.T.B. Mk 31 Torpedo 
Director, Report 330-1706-154, Oct. 5, 1943. 

Stabilizer for Torpedo Director Mark 30, OSRD 508(), 
Report 330-1706-162, February 1944. 

Study of Apparent Length Method for Aiming Air-Borne 
Torpedoes, Report 330-1706-169, July 8, 1944. 

Analysis of Films from Project 7-43, A.A.U., U.S. 
Naval Air Station, Norfolk, Virginia, Report 330-1706- 
170, Mar. 29, 1944. 

Torpedo Director Mark 32, R. W. Pitman, OSRD 5079, 
OEMsr-330, NO-106, Report 330-1706-172, Jan. 26, 
1944. Div. 7-141-Ml 

Linear Target Track Errors Caused by Accidental Devi- 
ation from Horizontal of the Flight Path of a Torpedo 
Plane, Report 330-1706-175, May 3, 1944. 

Torpedo Director Type B-3, OSRD 6223, Report 330- 
1706-180, May 15, 1944. 

Combination Torpedo Director, Fixed Gun Sight and Bomb 
Sight {NO-241), OSRD 6576, Report 330-1706-195, 
Nov. 13, 1944. 


24. 

25. 

26. 

27. 

28. 

29. 

30. 

31. 

32. 

33. 

34. 

35. 

36. 

37. 

38. 

39. 

40. 

41. 

42. 




238 


BIBLIOGRAPHY 


43. Range Type Torpedo Director, Report 330-1706-196, 
Oct. 19, 1945. 

44. Apparent Length Method for Aiming Tossed Torpedoes, 
Report 330-1706-201, Nov. 27, 1944. 

45. Torpedo Director for Maneuvering Targets, Report 330- 
1706-226, Nov. 16, 1945. 

46. Torpedo Trainer Computer, Report 330-1706-227, 
October 1945. 


The following reports were issued by the Statistical Research 
Group, Columbia University; 

47. Lead Angles for Aerial Torpedo Attacks Against Turning 

Ships, OEMsr-618, AMP Report 8.1R, SRG Report 190, 
July 1944. AMP-405.1-M6 

48. Tables of Aircraft Torpedo Lead Angles, OEMsr-618, 
AMP Report 8.2R, SRG Report 453, May 1945. 

AMP-405. 1-M9 


PART III 


1. Military Airborne Radar Systems, NDRC Summary 
Technical Report, Division 14, Vol. 2, Radiation Labora- 
tory, Massachusetts Institute of Technology. 

2. Analytical Studies in Aerial Warfare, NDRC Summary 
Technical Report, Applied Mathematics Panel, Vol. 2. 

3. Aerial Gunnery Problems, Saunders MacLane, AMG-C 
491, AMP, Aug. 31, 1945. 

4. Bibliography of Papers Written at the Applied Mathemaxic 

Group, Division of War Research, Columbia University, 
L. LaSala and M. Reiner, OEMsr-1007, AMG-C 496, 
October 1945. AMP-905.2-M2 

5. Pursuit Courses, Walter Leighton, [OEMsr-1007], 

AMG-C 141, AMP Memo 57.4, AMG-Columbia, Mar. 
29, 1944. AMP-503.7-M1 

6. Aerodynamic Lead Pursuit Curves, Daniel Zelinsky, 
[OEMsr-1007], AMG-C 273, AMG-Columbia, Sept. 29, 

1944. AMP-503.7-M8 

7. The Aerodynamic Pursuit Curve, IVl. M. Day and W. 
Prager, [OEMsr-1066], AMG-B Memo 31 M, AMP 
Memo 106.1M, AMG-Brown, July 12, 1944. 

AMP-503.7-M4 

8. Aerodynamic Lead Pursuit Curves for Overhead Attacks, 
G. H. Handelman and W. R. Heller, OEMsr-1066, 
AMG-B 79, AMP Report 106.2R, AMG-Brown, Oct. 31, 

1945. AMP-503.7-M15 

9. Equations for Aerodynamic Lead Pursuit Courses, Leon 

W. Cohen, OEMsr-1007, AMG-C 316, AMP 153.1R, 
AMG-Columbia, July 1945. AMP-503. 7-M12 

10. Aerodynamic Lead Pursuit Courses, Leon W. Cohen, 

OEMsr-1007, AMG-C 443, AMP 153.2R, AMG- 
Columbia, July 1945. • AMP-503.7-M11 

11. Interception and Escape Techniques at High Speed and 
High Altitudes, W. B. Klemperer, Report SM-3263 
(revised), Douglas Aircraft Company, Inc., Oct. 23, 1941. 

AMP-504.6-M1 

12. Graphs of Pursuit Curve Characteristics, N. V. Mayall, 
OEMsr-101, Carnegie Institute of Washington and 
Mt. Wilson Observatory, Apr. 5, 1944. 

AMP-503.7-M2 

13. Pursuit-Bomber Attack Calcidations, Report D.A. 71353, 
General Electric Company, Dec. 9, 1943. 

14. The Bank of an Airplane and Load Factor Under Condi- 

tions of General Flight, William M. Borgman, Jam Handy 
Organization, Inc., June 30, 1944. AMP-504.6-M2 

15. Experimental Determination of the Path of a Fighter Plane 
in Attacking a Bomber, Navy Contract N166s-2052, 
Jam Handy Organization, Inc., Mar. 13, 1944. 

16. The Current Status of the Simplest Attackability Problem, 

John W. Tukey, [OEMsr-1365], AMG-P Memo 12, 
AMG-Princeton, June 7, 1945. AMP-504.4-M14 

17. Firing Sidewise from an Airplane — /. Theoretical Con- 
siderations, H. P. Hitchcock, Report 1 16, Ballistic 

* 


Research Laboratory, Aberdeen Proving Ground, Aug. 
12, 1938. 

18. The Effect of Yaw Upon Aircraft Gunfire Trajectories, 
Theodore E. Sterne, Report 345, Ballistic Research 
Laboratory, Aberdeen Proving Ground. 

19. Analytical Trajectories for Type 5 Projectiles, Theodore E. 
Sterne, Report 346, Ballistic Research Laboratory, 
Aberdeen Proving Ground. 

20. On the Motion of a Projectile with Small or Slowly Chang- 
ing Yaw, Report 446, Ballistic Research Laboratory, 
Jan. 29, 1944. 

21 . Analysis and Computation Procedures for 50 Cal. Machine 
Gun Ballistic Corrections, Report DF-71342, General 
Electric Company, Aug. 14, 1942. 

22. Simple Formulas to Fit the Values Tabulated in the Firing 

Tables FT 0.50 AC-M-1, George Piranian, OEMsr-1007, 
AMG-C 130, AMP Memo 104.1, AMG-Columbia, 
Apr. 6, 1944. AMP-503. 1-M2 

23. Ballistic and Defection Formulas for Aerial Gunnery, 
Alex E. S. Green, Laredo Army Air Field Research 
Bulletin 106, AMP Memo 104.2M, June 27, 1944. 

AMP-503. 1-M6 

24. On Direct Firing Tables for Flexible Aircraft Gunnery, 
with Particular Reference to Caliber 0.50 A.P. M2 
Ammunition, Theodore E. Sterne, Report 396, Ballistic 
Research Laboratory, Aberdeen Proving Ground, Sept. 
2, 1943. 

25. Deflection Formulas for Airborne Fire Control, Magnus R. 

Hestenes, OEMsr-1007, AMG-C 247R, AMP 104.2R, 
AMG-Columbia, October 1945. AMP-503.3-M8 

26. The Problem of True Lead Under Evasive Action {Two- 
Dimensional Case), [OEMsr-1007], AMG-C 235, AMP 
Study 104, AMG-Columbia, July 25, 1944. 

AMP-503.6-M29 

27. Tables of True Leads for Two Pure Pursuit Courses, 
Irving Kaplansky, [OEMsr-1007], AMG-C 222, AMP 
Study 104, AMG-Columbia, July 8, 1944. 

AMP-503.6-M26 

28. Tables Giving True Lead for Three Pure Pursuit Courses, 
Gustav A. Hedlund, [OEMsr-1007], AMG-C 231, AMP 
Study 104, AMG-Columbia, Jul}^ 20, 1944. 

AMP-503.6-M28 

29. Some Uses of Variable Speed Mechanisms In Fire Control, 
Magnus R. Hestenes, OEMsr-1007, AMG-C 149, AMP 
Memo 103.1, AMG-Columbia, Apr. 14, 1944. 

AMP-503.1-M3 

30. Gyroscopic Lead Computing Sights, Report to the Services, 

Aug. 13, 1941. Div. 7-112.11-Ml 

31. Solution of the Differential Equation, {—a{d\/dt) + 

{1/u) \ = da/dt,) Walter Leighton, [OEMsr-1007], 
AMG-C 142, AMP Memo 57.5, AMG-Columbia, Mar. 
29, 1944. AMP-503.6-M19 




NFIDENTIAL 


BIBLIOGRAPHY 


239 


32. An Alternate Method for Solving the Equation, {—a{d\/ 
dt) + (1/w) X = da/dt,) Magnus R. Hestenes, [OEMsr- 
1007], AMG-C 179, AMG-Columbia, May 24, 1944. 

AMP-13-M14 

33. Conversion Formulas for Elevation and Traverse Leads, 

[OEMsr-1007], AMG-C 121, AMP 54.1, AMG-Columbia, 
E. J. Poitras, March 1944. AMP-503.6-M14 

34. Tables of Errors Committed When Using N-8 Sight with 

Position Firing Rules Against Three Pure Pursuit Courses, 
[OEMsr-1007], AMG-C 234, AMP Study 104, AMG- 
Columbia, July 21, 1944. AMP-503.4-M2 

35. Emergency Sighting Rules for Gunners on B-29 Bombers, 
Alex E. S. Green, Laredo Army Air Field Research 
Bulletin 104, July 4, 1944. 

36. Position Firing Rules for the A-26, Dan Zelinsky, 

OEMsr-1007, AMG-C 331, AMP Memo 119.2M, AMG- 
Columbia, March 1945. AMP-503.4-M7 

37. On Apparent Speed Firing, Charles Nichols, OEMsr- 

1379, AMG-N 80, AMP Memo 157.2M, AMG-North- 
western, Aug. 17, 1945. AMP-503.4-M11 

38. Own Speed Sights, Alex E. S. Green and George W. 
Taylor, Laredo Army Air Field Research Bulletin 101, 
July 1, 1944. 

39. Tail Gun Compiding Sight, KIO {Revised), E. B. Ham- 
mond, Sperry Gyroscope Company, Inc., Mar. 16, 1943. 

AM P-502. 1-M4 

40. Nose Computing Sight {K-11), B. L. Allison, Sperry 
Gyroscope Company, Inc., Aug. 4, 1943 (revised July 7, 
1944). 

41. Preliminary Instructions, Sperry Compensating Sights, 
Types K-10 and K-11, Instruction 14-223A, Sperry 
Gyroscope Company, Inc., December 1943. 

42. Vector Gunsights and Assessing Cameras, OSRD 5646, 
Report to the Services 96, Jam Handy Organization, Inc., 
Sept. 30, 1945. 

43. The Army Vector Sight Manual, AAF Contract W33- 
038-ac835, Jam Handy Organization, Inc., Sept. 29, 1944. 

44. Conversion of B-17 Stinger Sight Into an Own Speed Sight 
by Changing Pulley Ratio, R. V. Churchill, Laredo Army 
Air Field Research Bulletin 102, July 1, 1944. 

45. An Experimental Own-Speed Gunsight, Edward F. Allen, 
OSRD 5083, Report 330-1706-911, Franklin Institute, 
Sept. 28, 1944 (revised Sept. 26, 1945). 

46. Judgment of Attack and Support Situations in the Air, 
Laredo Army Air Field Research Bulletin 134, May 24, 
1945. 

47. Judgment of Aspect Angles, Laredo Army Air Field 
Research Bulletin 121, Sept. 30, 1944. 

48. Use of Compensating Sights Including the Problem of 
Support Fire, Laredo Army Air Field Research Bulletin 
135, June 25, 1945. 

49. Position Firing Rules for Support Fire with a Vector Sight, 
Charles Nichols, AMG-N 37 (revised), AMP Memo 
157. IM, AM G-North western. Mar. 19, 1945. 

50. ^ Instructions for Sperry Compensating Sight, Type K-13, 
* Sperry Gyroscope Company, Inc., Instruction 14-224, 

March 1944. 

51. A Comparison of True Leads and the Leads Produced by 

the K-13 Sight for Three Pure Pursuit Courses, Gustav A. 
Hedlund, [OEMsr-1007], AMG-C 241, AMP Study No. 
104, AMG-Columbia, Aug. 2, 1944. AMP-503.6-M31 

52. What 'Percent of Own Speed Deflection? Gustav A. Hed- 


lund, [OEMsr-1007], AMG-C 270, AMP 119.1R, AMG- 
Columbia, November 1944. AMP-503.3-M3 

53. Average Percentages of Own Speed Deflection, Dan 
Zelinsky and M. J. Lewis, OEMsr-1007, AMG-C 354, 
AMP Memo 119.1M, AMG-Columbia, January 1945. 

AMP-503.3-M4 

54. Optimum Methods of Using Compensating Sights, Dan 

Zelinsky, OEMsr-1007, AMG-C 472, AMP 119.2R, 
AMG-Columbia, October 1945. AMP-502.12-M20 

55. An Introduction to the Analytical Principles of Lead 

Computing Sights {Corrected Preliminary Form), Saunders 
MacLane, AMG-C 137, AMP Memo 55.1M, AMG- 
Columbia, April 1944. AMP-503.6-M21 

56. Sperry .50 Calibre Automatic Computing Sights {Types 
K-3, K-4, K-5), Sperry Gyroscope Company, Inc., 
Instruction 14-225, December 1941. 

57. K-3 and K-4 Aircraft Sight Error Analysis, Edmund B. 

Hammond, Jr., Sperry Gyroscope Company, Inc., 
May 3, 1944. AMP-502.11-M2 

58. Preliininary Instructions, Sperry Computing Sight, Type 
K-12, Sperry Gyroscope Company, Inc., Instruction 
14-240, July 1944. 

59. Bias Errors of the K-3 and K-12 Sights, Irving Kaplansky 
and Mae Reiner, OEMsr-1007, AMG-C 368, AMP 
Memo 104.3M, AMG-Columbia, May 1945. 

AMP-502.11-M13 

60. Theory of Gunsight Mark 14, C. S. Draper and E. P. 
Bentley, Sperry Gyroscope Company, Inc. 

61. Errors in Two Gyro Lead Computing Sights, [OEMsr- 

1007], AMG-C 66, AMP Study 72, AMG-Columbia, 
Oct. 13, 1943. AMP-503.6-M7 

62. Summary of Sights of the Mark 18 Family, Irving Kap- 

lansky, [OEMsr-10071, AMG-C 459, AMP Study 155, 
AMG-Columbia, July 6, 1945. AMP-502.12-M19 

63. Service Manual for Gun Sight Mark 18 and Mods., 
Bureau of Ordnance, Navy Department, Ordnance 
Pamphlet 1043, September 1943. 

64. Mark 18 Gun Sight, Research Technical Report 7, Lukas- 
Harold Corporation, Aug. 15, 1944. 

65. Design and Calibration of Mark 18 Sight Computer, 
Research Technical Report 9-A, Lukas-Harold Corpora- 
tion, Aug. 15, 1944. 

66. Theoretical Analysis of the Performance of Gyroscopic 
Gunsights of the Mark 18 Type, OSRD 5976, Report 
330-1706-198, Report to the Services 99, Franklin Insti- 

• tute, Nov. 30, 1944. 

67. Solution of the Equations for the Behavior of the Mark 18 
Gunsight when Tracking an Arbitrary Space Course, 
Donald P. Ling, OEMsr-1007, AMG-C 238, AMP 
Study 104, AMG-Columbia, July 28, 1944. 

AMP-503.2-M11 

68. The Theory of an Electro-Magnetically Controlled Hooke’s 
Joint Gyroscope, Donald P. Ling, OEMsr-1007, AMG- 
C 262, AMP 104.3R, AMG-Columbia, October 1945. 

AMP-502. 1-M34 

69. The Optical System of the Mark 18 {K15) Gijro Gunsight, 
L. Charles Hutchinson, OEMsr-1007, AMG-C 261, 
AMP 104.5R, AMG-Columbia, October 1945. 

AMP-502. 12-M23 

70. Deflection Formulas for Gun Sights of the Mark 18 Type, 
Donald P. Ling, [OEMsr-1007], AMG-C 358 (revised), 
AMP Study 104, 165, AMG-Columbia, June 26, 1945. 

AMP-503.3-M7 


IDENTIAL 




240 


BIBLIOGRAPHY 


71. The Behavior of the Mark 18 Sight on Pure Pursuit 
Courses, Irving Kaplansky, [OEMsr-1007], AIVIG-C 264, 
AMP Study 104, AMG-Columbia, Sept. 20, 1944. 

AMP-502. 12-M6 

72. Bias Errors of the Interiyn Mark 18 {K15), Irving Kap- 

lansky, OEMsr-1007, AMG-C 367, AMP Study 104, 
AMG-Columbia, Feb. 14, 1945. AMP-502. 12-M 12 

73. Tests of the Gunsighi MK 18, Lloyd A. Jeffress and 
Lawrence E. Brown, OSRD 4979, Report to the Services 
91, The University of Texas, Oct. 22, 1945. 

74. The Calibration of the Mark 18, Irving Kaplansky, 

[OEMsr-1007], AMG-C 272, AMP Study 104, AMG- 
Columbia, Sept. 28, 1944. AMP-502. 12-M7 

75. A General Principle Regarding the Design of Instruments, 

with Special Reference to Lead-Computing Sights, George 
Piranian, OEMsr-1007, AMG-C 239, AMP Study 104, 
AMG-Columbia, Aug. 8, 1944. AMP-503.6-M32 

76. The Time of Flight Setting of a Lead Computing Sight, 
Irving Kaplansky, OEMsr-1007, AMG-C 351, AMP 
Memo 155. IM, AMG-Columbia, March 1945. 

AMP-503.6-M38 

77. Tracking and Gun Errors Over a “Cross-Over” Course 
with Variation of Time-of -Flight Setting Appropriate to 
Range, Report 330-1706-208, Franklin Institute, Aug. 2, 
1945. 

78. Tracking and Gun Errors Observed with Extreyne Values 
of “a” of the Lead Computing Sight with Two Kinds of 
Turret Control, Report 330-1706-225, Franklin Institute, 
Oct. 17, 1945. 

79. Second Report on Tracking and Gun Errors Over a 
“Crossover” Course with Variation of Time-of -Flight 
Setting Appropriate to Range, Report 330-1706-230, 
Franklin Institute, Oct. 15, 1945. 

80. Final Report on Test of Evaluation of Aerial Guns and 
Gun Sights, Hqs. Army Air Forces Proving Ground 
Command, Eglin Field, Florida, Serial 2-44-22, AAF 
Board Project F3270, Jan. 29, 1945. 

81. Errors Made by a Lead-Computing Sight When the Target 
Follows a Pursuit Course, Walter Leighton, AMG-C 82, 
AMP 57.1, AMG-Columbia, December 1943. 

AMP-503.6-M8 

82. Graphical Summaries of the Mechanism Errors of Various 

Airborne Fire Control Systems, [OEMsr-1007], AMG-C 
300 (revised), AMP Study 104, AMG-Columbia, Dec. 
14, 1944. AMP-503. 1-M9 

83. An Analytic Study of the Performance of Airborne Gun 
Sights, Donald P. Ling, OEMsr-1007, AMG-C 440, 
AMP 104. IR, AMG-Columbia, June 1945. 

AMP-502. 1-M25 

84. Fairchild Type S-3 Gyro Computing Sight, Fairchild 
Camera and Instrument Corporation, September 1944. 

85. Lead Formulas for the Fairchild S-3 Sight, Magnus R. 
Hestenes and Dan Zelinsky, [OEMsr-1007], AMG-C 363, 
AMP Study 104, AMG-Columbia, Feb. 7, 1945. 

AMP-502. 13-M9 

86. More on the Gyro Error in the S-3, E. R. Lorch, [OEMsr- 

1007], AMG-C 419, AMP Study 104, AMG-Columbia, 
May 21, 1945. AMP-502. 13-M 16 

87. Preliminary Analysis of the S-4 Sight, E. R. Lorch and 

• Dan Zelinsky, [OEMsr-1007], AMG-C 451, AMP Study 
104, AMG-Columbia, July 7, 1945. AMP-502. 13-Ml 9 

88. The Sperry S-8B Stabilized Sight, Samuel Eilenberg, 

[OEMsr-1007], AMG-C 420, AMP Study 1C4, AMG- 
Columbia, May 22, 19-^5. AMP-502. 13-M17 


89. Computers for Radar Control of Plane-to-Plane Gunfire, 
John B. Russell and James C. Sheridan, NDRC Division 
14 Report 130, Radiation Laboratory, Massachusetts 
Institute of Technology, March 15, 1943. 

Div. 14-323.1-Ml 

90. Radar Gun-Laying System Final Technical Report, 

OEMsr-233, NDRC Division 14 Report 385, General 
Electric Company, 1944. Div. 14-323. 13-M4 

91. [The] 2 CHlAl Aircraft Fire Control Computer, Supple- 
ment to Final Technical Report, Dan L. Colbath, OEMsr- 
233, NDRC Division 14 Report 570, Report 45813, 
General Electric Company, Nov. 16, 1945. 

Div. 14-323.13-M3 

92. Operation and Service Instructions for the Central Station 
Fire Control System, AAF Technical Order AN-70A-20, 
May 30, 1945. 

93. Handbook of Instructions with Parts Catalogue for Re- 
strained-Type Gyros, AAF Technical Order AN-70A-25, 
May 15, 1945. 

94. Handbook of Instructions with Parts Catalogue for Com- 

puters in Central Station Fire Control Systems, AAF 
Technical Order AN-70A-9, General Electric Company, 
June 10, 1945. AMP-503.5-M8 

95. General Principles of the General Electric CFC Computer: 

Models 2CH1C1 and 2CH1D1, Magnus R. Hestenes, 
Daniel C. Lewis, and F. J. Murray, OEMsr-1007, 

AMG-C 346, AMP Memo 143. IM, AMG-Columbia, 
September 1945. AM P-503. 5-M 14 

96. Gyroscopes of the General Electric CFC Computer in the 
B-29 Airplane, Magnus R. Hestenes, Daniel C. Lewis, 
and F. J. Murray, OEMsr-1007, AMG-C 345, AMP 
Memo 143.2M, AMG-Columbia, September 194^ 

AMP-503.5-M12 

97. The Axis Converter and the Potentiometer Resolver in the 

General Electric B-29 Computer, Magnus R. Hestenes, 
Daniel C. Lewis, and F. J. Murray, OEMsr-1007, 

AMG-C 346.1, AMP Memo 143.3M, AMG-Columbia, 
September 1945. AMP-503.5-M13 

98. Free Gyro Lead Computer, Report 45751, General Elec- 
tric Company, July 21, 1944. 

99. G.E. Gyro Stabilized Sight with Lead Control for Remote 

Control Turrets, J. R. Moore, Report 31298, General 
Electric Company, Sept. 12, 1944. AMP-502.1-M14 

100. A Suggestion for Improving the Performance of the B-29 

2CH1C1 Computer, Magnus R. Hestenes and Daniel C. 
Lewis, OEMsr-1007, AMG-C 391, AMP Study 143, 
AMG-Columbia, Mar. 24, 1945. AMP-503.5-M4 

101. Further Modifications of the B-29 Fire Control Computer, 

Magnus R. Hestenes and Daniel C. Lewis, [OEMsr- 
1007], AMG-C 391a, AMP Study 143, AMG-Columbia, 
Mar. 27, 1945. AMP-503.5-M5 

102. A Proposal for Controlling the Speeds of the Total Correc- 

tion Motors in the General Electric 2CH1C1 Computer, 
Magnus R. Hestenes, Daniel C. Lewis, and F. J. Murray, 
[OEMsr-1007], AMG-C 453, AMP Study 188, AMG- 

Columbia, July 5, 1945. AMP-503.5-M9 

103. Remarks with Regard to Modifications oj the Present B-29 

Computer, Magnus R. Hestenes and Daniel C. Lewis, 
[OEMsr-1007], AMG-C 455, AMP Study 188, AMG- 
Columbia, July 5, 1945. AMP-503. 5-M 10 

104. Ranging in Defense of the B-29 Against Nose Attacks, 
Daniel C. Lewis, [OEMsr-1007], AMG-C 394R, AMP 
Study 188, AM(l-Columbia, June 30, 1945. 

AMP-503.2-M25 


^Fonfidenti^ 


BIBLIOGRAPHY 


241 


105. Test of G.E. Fire Control Equipment in B-29 Airplane, 
Army Air Forces Board, Project (M-l)lOc, June 20, 1944. 

106. Ground Tests of the B-29 Central Fire Control System, 
W. D. Crozier, OEMsr-1390, AC-92, UNM/\V/TR5, 
LTniversity of New Mexico, Jan. 15, 1945. 

AMP-503.5-M3 

107. Tests of B-29 Computers for Nose Defense on the Uni- 
versity of Texas Testing Machine, Edwin Hewitt and 
William L. Duren, Operations Analysis Division, Head- 
quarters Twentieth Air Force, Apr. 28, 1945. 

108. Calibration of the B-29 Computer for Tail Defense, 
Edwin Hewitt, Operations Analysis Division, Head- 
quarters Twentieth Air Force, July 4, 1945. 

109. Tests of Modifications of the G.E. B-29 C.F.C. System, 
Lloyd A. Jeffress, War Research Laboratory, University 
of Texas, Nov. 22, 1945. 

110. Sperry AGL-2 Equipment, Instruction 23-165, Sperry 
Gyroscope Company, Inc., March 1943. 

111. Preliminary Instructions, Sperry Central Fire Control 
System for B-29 Airplane, Instruction 14-212, Sperry 
Gyroscope Company, Inc., September 1943. 

112. The Sperry Stabilized Aircraft Gun Laying System, Inter- 
mediate Phase, NDRC Division 14 Report 289, Sperry 
Gyroscope Company, Inc., May 1944. 

Div. 14-323. 13-M2 

113. Report on NDRC Coritract OEMsr-812, [The Fairchild 

Central Station Computer], OEMsr-812, NDRC Divi- 
sion 14 Report 433, Fairchild Camera and Instrument 
Corporation, Apr. 30, 1945. Div. 14-323. 12-M6 

114. The Remote Control of Guns in Aircraft: An Account of 
an Experimental Armament Installation in a Lancaster 
Aircraft, Royal Aircraft Establishment, Farnborough, 
Technical Note Arm. 269 (F.C.), February 1944. 

115. Report on Preliminary Trials of an Experimental Arma- 
ment in a Lancaster Aircraft, Royal Aircraft Establish- 
ment, Farnborough, Tech. Note Arm. F.C. 308, October 
1944. 

116. Final Report on Tracking Studies, Report 330-1706-232, 
Project NO-268, Franklin Institute, Nov. 15, 1945. 

117. Exploratory Experiments on Tracking with Lead Comput- 
ing Sight, Report 330-1706-151, Project 1706-2A, 
Franklin Institute, Aug. 14, 1943. 

118. Tracking Errors in Systems Using Velocity-Tracking and 

Aided-T racking Controls with Direct and Lead-Computing 
Sights, OEMsr-330, Report to the Services 78, Franklin 
Institute, February 1944. AMP-503.2-M3 

119. Errors in Tracking with a Lead-Computing Sight under a 
Variety of Conditions of “a” Time-of -Flight Setting, Aided- 
Tracking Constant, and Rate Control, Report 330-1706- 
159, Franklin Institute, May 11, 1944. 

120. Analyses of Tracking and Gun Errors Relative to the 
Operators Judgment and the Use of the Trigger. A. Analy- 
ses of Aided-T racking Records, Report 330-1706-204, 
Project NO-268, Franklin Institute, May 30, 1945. 

121. Analyses of Tracking and Gun Errors Relative to the 
Operator’s Judgment and the Use of the Trigger. B. Analy- 
ses of Velocity-Tracking Records. C. Comparison of Aided 
and Velocity Tracking Records, Report 330-1706-217, 
Project NO-268, Franklin Institute, Aug. 27, 1945. 

122. Preliminary Report on Tracking and Gun Errors Observed 
in a Martin Turret with Maxson Controls Providing a Vari- 
ety of Aided-T racking Time Constants, Report 330-1706- 
210, Project NO-268, Franklin Institute, 

Mar. 31, 1945. 


123. Experimental Study of Tracking and Gun Errors Observed 
in a Martin Turret with Maxson Controls Providing 
Sixteen Combinations of Tracking Controls, Report 330- 
1706-231, Project NO-268, Franklin Institute, Nov. 7, 
1945. 

124. The Performance of the Lead-Computing Sight with Aided- 
and with Velocity-Tracking Control under Optimal Con- 
ditions of Practice, Report 330-1706-214, Project NO-268, 
Franklin Institute, Oct. 17, 1945. 

125. Tracking Tests with the G.E. Ring Sight, G.E. Pedestal 
Sight, and the Sperry Turret with Fixed Sight, War Re- 
search Laboratory, University of Texas, June 24, 1944. 

126. Camera Tracking in Simulated Aerial Defense Gunnery, 
I. The K-3 Sight in the Sperry Upper Local Turret and 
the Flexible Gun, II. The N-6 Sight in the Martin Upper 
Local Turret and the Flexible Gun, Department of 
Physics, University of New Mexico. 

127. Tests Related to the Defense and Tactical Use of the B-29, 
R. E. Holzer, OEMsr-1390, AC-92, UNM/W/TR3, 
University of New Mexico, Nov. 15, 1944. 

AMP-504.41-M3 

128. Airborne Tracking and Ranging Errors, Arthur Sard, 

OEMsr-1007, AMG-C 488, AMP Memo 166.2M, AMG- 
Columbia, October 1945. AMP-503.2-M27 

129. Handbook of Operating Instructions for AN/APG-5, 
Navy Manual, AN-16-30 APG 2, Mar. 20, 1945. . 

130. Preliminary Instruction Manual for AN / APG-15B, J. 

Vance Holdam, Jr., OEMsr-262, SC-69, Report M-215, 
Radiation Laboratory, Massachusetts Institute of 
Technology, June 1, 1945. Div. 14-323. 12-M8 

131. Radar Fire Control Developments for Military Aircraft, 
Armament Section, AC/AS-4, Apr. 1, 1946. 

132. Tracking Studies, Mechanization, Instrumentation and 
Control, Report 330-1706-126, Franklin Institute, Oct. 
15, 1942. 

133. Tracking Unit Number Two, Report 330-1706-197, 
NO-268, Franklin Institute, Oct. 10, 1945. 

134. Tracking Unit Number 3, or an Electronic Tracking Study 
Mechanism for Use with Lead-Computing Sights in Com- 
bination with Turrets, Report 330-1706-215, NO-268, 
Franklin Institute, Oct. 31, 1945. 

135. An Investigation of the Operator’s Response in Manual 
Control of a Power Driven Gun, A. Tustin, Memorandum 
169, Metropolitan- Vickers Electrical Co. Ltd., Atter- 
cliffe Common Works, Sheffield, C. S., Aug. 22, 1944. 

'136. Final Report, Columbia University, Division of War 
Research, OEMsr-1237, Oct. 12, 1945. 

137. Memorandum on the Testing of Plane-T o-Plane Fire- 
Control Devices and Systems, NDRC Section D-2, July 
24, 1942. 

138. Memorandum on Testing Machine Design, NDRC Sec- 
tion D-2, July 25, 1942. 

139. Development of a Machine for Testing Airborne Gunnery 
Systems, Lucien La Coste, War Research Laboratory, 
University of Texas, Dec. 15, 1943. 

140. Progress Report on the Development of a Machine for 
Testing Airborne Gunnery Systems, Lucien La Coste, 
War Research Laboratory, University of Texas, July 15, 
1944. 

141. Progress Report on Turret, Target, and Projector Systems, 
R. T. Cloud, Stanolind Oil and Gas Company, Explora- 
tion Research Laboratory, Sept. 9, 1944. 

142. Progress Report on Proposed Cross Film System for 
Introducing Target and True Gun Motion for the Plane 


k i CONFIDENTIAL 


242 


BIBLIOGRAPHY 


to Plane Fire Control Testing Equipment, Stanolind Oil 
and Gas Company, Exploration Research Laboratory, 
Sept. 1, 1944. 

143. Progress Report on Proposed Cross Film System j’or Intro- 
ducing Target and True Gun Motion for the Plane to Plane 
Fire Control Testing Equipment, Stanolind Oil and Gas 
Company, Exploration Research Laboratory, Oct. 19, 
1944. 

144. Report on Gun Position Recording, R. T. Cloud, Stanolind 
Oil and Gas Company, Exploration Research Labora- 
tory, May 19, 1943. 

145. Photographic Method of Recording Error for the Plane to 
Plane Gun Fire Testing Machine, Jack Cooper, Stanolind 
Oil and Gas Company, Exploration Research Labora- 
tory, May 18, 1943. 

146. Parallel Coordinate Target AN Gun Recording System, 
R. T. Cloud, Stanolind Oil and Gas Company, Explora- 
tion Research Laboratory, Sept. 14, 1943. 

147. Final Report on the Service Trials of the MK. II Gyro 

Gunsight for Turrets, OSRD Liaison Office II-5-5807 (S.) 
EX/GRU/47, Gunnery Research Unit, Exeter, Apr. 8, 
1943. AMP-502. 12-Ml 

148. Use of the Index as a Figure of Merit in Air Gunnery, 
EX/GRl^/46, Gunnery Research Unit, Exeter, Feb. 
8, 1943. 

149. Calculation of the Index from Cine Gun Trials, Appendix 
^‘A” to GRU/M4, Gunnery Research Unit, Exeter, 
July 25, 1943. 

150. The Cine-Gyro Assessor, GRU/M.2, Gunnery Research 
L^nit, Exeter, Mar. 26, 1943. 

151. Descriptive Note on G.G.S. Recorder Mk. 1 {Aiming Point 
Camera), Tech. Note Arm. 259, Royal Aircraft Establish- 
ment, Farnborough, February 1944. 

152. Preliminary Report on AC 115, A. A. Albert, AMG-N 44, 
AMP Study 166, AMG-Northwestern, Apr. 6, 1945. 

153. Results of a Recomputation of Sight Evaluation Test Data, 
Wallace Givens, OEMsr-1379, AMG-N 79, AMP Study 
166, AMG-Northwestern, Aug. 23, 1945. 

AMP-502.141-M10 

154. A Modified Computation Procedure for Camera Bomber 
Sight Assessment, A. A. Albert, AMG-N 47, AMP Study 
142-166, AMG-Northwestern, May 2, 1945. 

155. Gnomonic Charts, A. A. Albert, AMG-N 38, AMP Study 
142, AMG-Northwestern, Mar. 8, 1945. 

156. A Manual for the Use of Gnomonic Charts, A. A. Albert, 

OEMsr-1379, AMG-N 62, AMP Note 23, AMG-North^ 
western, October, 1945. AMP-503. 1-M14 

157. Camera Evaluation of Bomber Gun Sights, A. A. Albert, 

OEMsr-1379, AMG-N 50, AMP Study 142, AMG- 
Northwestern, May 23, 1945. AMP-502.14-M9 

158. Determination of Directions in Space by Photographs of 

Two or Three Fixed Points, A. A. Albert, OEMsr-1379, 
AMG-N 56, AMP Study 157, AMG-Northwestern, 
June 20, 1945. AMP-502. 14-M8 

159. Gyro Measurement of Rotations of Axes, A. A. Albert, 
AMG-N 36, AMP Study 166, AMG-Northwestern, 
Mar. 2, 1945. 

160. Gyro Measurement of Rotations, P. A. Smith, [OEMsr- 

1007], AMG-C 405 (revised), AMP Study 166, AMG- 
Columbia, June 7, 1945. AMP-502. 142-M2 

161. Roll, Pitch, Yaw Correction by Table, R. L. Swain, 

[OEMsr-1007], AMG-C 433, AMP Study 166, AMG- 
Columbia, June 4, 1945. AMP-502. 142-Ml 

162. Yaw, Pitch and Roll and the Horizon Ca??iem,^MG-N 16, 


AMP Study 142, AMG-Northwestern, Nov. 27, 1944. 

163. Final Report, Aerial Gunnery Assessment {Photographic 
Method), OEMsr-1276, Northwestern University, Oct. 
31, 1945. 

164. Computers Manual for Processing Aerial Gunnery- 
Assessment Film, NOa(s) 7632, Project 22, Northwestern 
University, Vol. 2. 

165. The Stereographic Spherimeter, L. Charles Hutchinson 
and John H. Lewis, OEMsr-1007, AMG-C 290, AMP 
Memo 107. IM, AMG-Columbia, January 1945. 

AMP-503-M3 

166. Correction for Roll, Pitch and Yaw with the Spherimeter, 

L. Charles Hutchinson and John H. Lewis, OEMsr-1007, 
AMG-C 366, AMP Memo 107.2M, AMG-Columbia, 
February 1945. AMP-503-M4 

167. Kinematic Lead Under Evasive Action and Its Determina- 
tion by Photography from the Bomber, Preliminary Note, 
R. S. Wolfe, [OEMsr-1007], AMG-N 48, AMP Study 
172, AMG-Northwestern, May 10, 1945. AMP-503.6-M39 

168. Proposed Evaluation Test Program of the B-29 Armament 
System, General Electric Company, July 6, 1944. 

169. A Method of Analyzing Aerial Gun Camera Film Based 

on Use of Distant Reference Points, G. T. Pelsor, OEMsr- 
1390, AC92, UNM/W-32, University of New Mexico, 
Apr. 14, 1945. AMP-502.14-M7 

170. The Air Mass Coordinate Method of Aerial Gunnery 
Assessment, E. G. Pickets, Feb. 15, 1945. AMP-503.3-M5 

171. Application of the Air Mass Coordinate Method to Aerial 
Gunnery Assessment, P. A. Smith, [OEMsr-1007], AMG-C 
471, AMP Study 187, AMG-Columbia, July 27, 1945. 

AMP-502. 1-M29 

172. Frangible Bullets and Aerial Gunnery, Gustav A. Hed- 

lund, OEMsr-1007, AMG-C 422, AMP Memo 167.1M, 
AMG-Columbia, July 1945. AMP-504.52-M5 

173. A Proposed Device for Fighter Fihn. Assessment, Samuel 
Eilenberg and John H. Lewis, [OEMsr-1007], AMG-C 
404, AMP Study 104, AMG-Columbia, Apr. 20, 1945. 

AMP-504.51-M13 

174. Camera Assessment of Fighter Plane Gunsights, H. L. 
Garabedian, OEMsr-1379, AMG-N 52 (revised), AMP 
Study 160, AMG-Northwestern, Sept. 12, 1945. 

AMP-502. 14-M 14 

175. Computational Procedures and Forms for Camera Assess- 

ment of Fighter Plane Gunsights, R. S. Wolfe, OEMsr- 
1379, AMG-N 84, AMP Study 160, AMG-Northwestern, 
Sept. 5, 1945. ’ AMP-502. 14-M 12 

176. Measurement of Angle of Attach and Skid in Rocket Fire 

Problems, H. L. Garabedian, OEMsr-1379, AMG-N 61 
(revised), AMP Study 191, AMG-Northwestern, Sept. 
12, 1945. AMP-502. 14-M 13 

177. Improvements in a Method of Skid Measurement, H. L. 
Garabedian, AMG-N 76, AMP Study 191, AMG- 
Northwestern, Aug. 10, 1945. 

178. Computational Procedures and Forms for Measurement of 
Angle of Attack and Skid in Rocket Fire Problems, R. S. 
Wolfe, AMG-N 81, AMP Study 191, AMG-North- 
western, Aug. 21, 1945. 

179. Notes on the Assessment of a Bomber's Defensive Fire, 
AMP Working Paper 1, October 1944. AMP-504.1-M15 

180. Bidlet Dispersion for B-17 and B-24 Aircraft, Research 
Bulletin 123, Research Division of AAF Central School 
for Flexible Gunnery, Laredo Army Air Field, Texas, 
Oct. 1, 1944. 

181. Bullet Dispersions in the B-29 Aircraft, Research Bulletin 



NFIDENTIAL 


BIBLIOGRAPHY 


243 


143, Research Division of AAF Central School for 
Flexible Gunnery, Laredo Army Air Field, Texas, 
Project 208, August 1945. 

182. Test Program for Bullet Dispersion Experiment on B-29 
Armameyit System, Research Division of AAF Central 
School for Flexible Gunnery, Laredo Army Air Field, 
Texas. 

183. A Figure of Ment for Sight-Turret Performance, Arthur 

Sard, [OEMsr-1007], AAIG-C 343, AMP Study 104, 
AMG-Columbia, Dec. 29, 1944. AMP-502. 1-M20 

184. Dispersion Patterns in Fire From Moving Aircraft, 
George Piranian, [OEMsr-1379], AMG-N 18, AMP 
Study 142, AMG-Xorthwestern, Dec. 5, 1944. 

AMP-502. 141-M3 

185. Relative Target Motion and Effective Dispersion, Rollin F. 

Bennett, [OEMsr-618], SRG 398, SRG-Columbia, Jan. 8, 
1945. AMP-502. 141-M5 

186. Computation of Single Shot Probabilities in Camera Sight 
Assessment, A. A. Albert, [OEMsr-1379], AMG-X 23, 
AMP Study 142, AMG-Xorthwestern, Jan. 5, 1945. 

AMP-502. 14-M5 


187. The Phenomenon of Aerial Awi-Wander: An Essay on its 
Mathematical Description, Statistical Measurement and 
Influence on Gunnery Performance, L. B. C. Cunning- 
ham, OSRD Liaison Office WA-2055-4A, Report 51, 
Air Warfare Analysis Section, Apr. 29, 1944. 

AMP-502.1-M9 

188. The Mathematical Theory of Air Combat, L. B. C. Cun- 

ningham, OSRD Liaison Office II-5-1042, Air Warfare 
Analysis Section. AMP-504. 1-M2 

189. An Analysis of the Performance of a Fixed-Gun Fighter, 

Armed with Guns of Different Calibres, in Single Home- 
Defence Combat with a Twin-Engined Bomber, L. B. C. 
Cunningham, E. C. Cornford, W. Rudoe, and J. Knox, 
British Liaison Code WA-382-4d, [Air Warfare Analysis 
Section], February 1940. AMP-504.1-M1 

190. The Mathematical Theory of Air Combat, SRG-C 2, 

AMP 2.2, Aug. 26, 1942. AMP-504.1-M4 

191. The Assessment of Gun-Camera Trials, Rollin F. Bennett 

and Arthur Sard, [OEMsr-1007 and OEMsr-618], 
AMG-C 370, SRG-C 440, AMP Study 166, AMG- 
Columbia, Mar. 28, 1945. AMP-502.14-M6 


CONFIDENTIAL 


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INDEX 


The subject indexes of all STR volumes are combined in a master index printed in a separate volume. For 
access to the index volume consult the Army or Navy Agency listed on the reverse side of the half-title page. 


Absolute angular rate determination 
see Angular rates in airborne aiming 
controls 

Aerial gunnerj' contracts listing, 177- 
178 

Aerial gunnery local control systems, 
192-197 

fixed sight systems, 192-193 
lead-computing sights, 194-197 
own-speed sights, 193-194 
Aerial gunnery i^erformance evaluation, 

209- 213 

bullet dispersion pattern, 213 
figure of merit, 213 
flight tests, 210-212 
frangible bullets, 212 
general assessment methods, 209-210 
])hotographic methods for flight tests, 
211-212 

simulation, 209 

University of New Mexico assess- 
ment method, 212 

University of Texas testing machine, 

210 - 211 

vector method, 212 
Aerial gunnery princiides, 185-191 
ballistic lead, 187-188 
bullet flight time, 187-188 
lead computation, 188-191 
target courses, 185-187 
true lead, 188 

Aerial gunnery remote control systems, 
198-203 

British system, 203 
early developments, 198-199 
Fairchild computer, 203 
General Electric system, 199-201 
need for remote-control systems, 198 
Sperry- systems, 201-202 
Westinghouse system, 203 
Aerial gunnery survey, 179-184 
assessment, 183-184 
British MK Il-d sight, 179 
central station systems, 182 
development history, 179-180 
estimating lead, 180 
lead-computing sights, 180 
])Osition firing rule, 180 
radar, 184 

recommendations for future work, 
184 

ring-and-bead sight, 179 
training, 182-183 
turret controls, 181-182 
Aerial gunnery tracking and ranging, 
204-208 

Army Air Forces tests, 206 
definition of terms, 204 
Franklin Institute studies, 205-206 
mechanical simulators, 205 
radar for gunlaying, 207-209 


range measurement, 204 
stabilization, 206-207 
tracking controls, 204-205 
turrets, 204 

University of New Mexico studies, 
206 

University of Texas studies, 206 
Aiming controls, multiple sight indices, 
29-30 

Aiming of bombs from airplanes 
see Bomb aiming from airplanes 
Aiming of torpedoes from airplanes 
see Torpedo aiming from airplanes 
Aiming processes, general theory, 9-22 
angle between vectors, 13-14 
angular rates, 11-12 
collision course, 13 
constant true bearing, 13 
feedback, 19-20 

instrumental character of airborne 
fire-control, 20-22 
kinematic lead computing, 15-16 
position vectors, 9-13 
projectile aiming prblem, 14-16 
pursuit course, 12-13 
space-time geometry, 16-17 
synchronous operations, 17-18 
target approach, 12-13, 18-19 
Aiming-control specifications, 149-150 
Aircraft fire-control, instrumental com- 
ponents 

see Instrumental components of air- 
borne fire-control 

Aircraft fire-control system (AFCS) 
Mark 4 

see Pilot’s universal sighting system 
(PUSS) 

Aircraft fire-control systems, future 
see Future of airborne fire-control 
systems 

Aircraft rocket sight Mark 2; 134, 140- 
141 

altitude, 141 
components, 141 • 

developmental models, 134, 140-141 
glide angle input, 141 
Aircraft rocket sight Mark 3; 135, 143- 
145 

accelerometer component, 143 
skid problem, 144 
Aircraft torpedo aiming 

see Torpedo aiming from airplanes 
Aircraft torpedo director course stabili- 
zation, 165-166 

Airplane dynamics simulation, 63-64 
Angular rate bombing methods 

see Bombing methods involving abso- 
lute angular rate 
Angular rate meters (absolute) 

see Angular rates in airborne aiming 
controls 


Angular rates in airborne aiming con- 
trols, 35-47 

captive gyro principle, 38-40 
captive gyro with capacitive deflec- 
tion detection, 44-45 
centrifugal tension as measurement 
criterion, 46-47 

errors in lead-computing sights, 195 
future possibilities, 47 
gyros for angular rate bombing, 40-43 
importance in instrumental tech- 
nique, 35-36 

lead computation principles, 190-191 
measurement methods, 36-38 
oscillatory captive gyro, 45-46 
PUSS gyro, 43-44 
Angular rotation time rates, 11-12 
Antiaircraft director M-9; 124-125 
Antisubmarine bombsight Mark 20; 
100-106 

design, 104-105 
modifications, 105-106 
operation, 103-104 
theory of method, 100-103 
Automatic regulators and tracking aids, 
27-28 

AZON bomb, 112-114, 121, 124, 217- 
227 

Ballistic computer (aerial gunnery), 
187-189, 214 

Bomb aiming from airplanes, 95-111 
bombing trainer, 99 
classical methods and instruments, 
99-100 

development projects, 95-99 
diving attack, 109-111 
extrapolating antisubmarine bomb- 
sight, 100-106 

ground speed computers, 96-97 
low-altitude blind bombing com- 
puter, 97 

methods involving absolute angular 
rate, 106-107 

Norden bombsight Mark 15; 100 
paths of constant releasability, 107- 
109 

preset computer, 97 
spacing computer, 98 
statement of problem, 96-97 
Z-bombing, 98 
Bomb (guided) control 
see Guided bombs, control 
Bomb trajectory equations, 116-119 
Bomber turret controls, 181-182 
Bombing, ground-controlled (GCB), 115 
Bombing methods involving absolute 
angular rate 

Mark III LLBS (British), 106 
Mark 23; 106 
Mark 27; 106-107 


246 


INDEX 


PUSS, 107 

Sniffer (FM radar), 106 
Bombs, table of constants, 119 
Bombsights 

Mark 20; see Antisubmarine bomb- 
sight Mark 20 

Norden bombsight Mark 15; 100 
British report on cyclic dynamical 
systems, 51 

British single-gyro sight (MK-II-C), 
180, 196 

British zone firing method, 180 
Bullet flight time (aerial gunnery), 
187-188 

Capacitor in instrumental techniques, 
158-159 

Cai)tive gyros, 38-46 
advantage, 39 

angular rate bombsight components, 
40-43 

capacitive deflection detection, 44-45 
definition, 38 
feedback loop, 40 
feedback technique, 42-43 
future, 47 

noise problem, 41-42 
operation techniques, 38, 39 
oscillatory type, 45-46 
l)ilot’s universal sighting system 
(PUSS) gyro, 43-44 
principle, 38-40 
rotor drives, 38-39 
strain gauge technique, 40-41 
CARP sight, 114,124 
Cathode feedback, 52-53 
Causal loop in tracking system, 24-26 
Centrifugal tension as measurement 
criterion, 46-47 

mass pair angular rate meter, 46 
pneumatic capturing system, 46 
Collinearity control, 119-121 
AZON bomb, 121 
bomber evasion, 121-122 
first guiding sight, 122-123 
RAZON bomb, 119 
terminal collinearity, 113-114 
Computers 

ballistic, 189-190, 214 
Fairchild, 203 

for PUSS, 135, 145, 153-156 
future for airborne fire-control, 214- 
215 

ground speed, 96-97 
low-altitude blind bombing, 97 
Mark 35; 134, 140-141 
Mark 36; 135, 143-145 
P-4; 201-202 
preset, 97 
spacing, 98 

standard B-29; 199-200 
toss bombing (PACT), 110-111, 155- 
156 

Constant releasability paths (equa- 
tions), 107-109 

Course stabilization for aircraft tor- 
pedo directors, 165-166 
CRAB sight, 112-113, 124 


see also RAZON bomb 


Differential analyzer solutions for guided 
bomb trajectories (AZON and 
RAZON), 217-227 

Differential analyzer solutions for ROC 
trajectories, 227-230 
Dive bombing, 109-111 
DBS system, 110-111 
Draper/Davis sight (Army A-1), 110 
proportional navigation, 110 
PUSS system, 110-111 
toss bombing, 110-111 
Dynamic computer for universal sight- 
ing system, 153-156 

Electronic simulation, 50-65, 123-124 
airjdane dynamics, 63-64 
bomb-guiding simulator origin, 123- 
124 

cyclic dynamical systems, 51-52 
feedback amplifiers, 52-54 
flare-bomb guiding, 58-61 
future development, 64-65 
nonlinear systems, 54-56 
pursuit-collision course plotter, 50 
television bomb guiding, 61-63 
time scale, 58 

Fairchild lead-computing sights, 181, 
197 

Feedback amplifiers in simulative devel- 
opments, 52-54 
cathode feedback, 52-53 
plate feedback, 52-53 
polarity reverser, 53 
Feedback processes, 19-20 
Fixed sight systems for flexible gun- 
nery, 192-193 

oi)tical reflector type sight, 192 
position firing rule, 192-193 
ring-and-bead sight, 179, 192 
Flare-bomb guiding simulation, 58-61 
manipulation, 59 
simulative presentation, 59-60 
Flexible gunnery, fixed sight systems 
see Fixed sight systems for flexible 
gunnery 

Flexible gunnery assessment, photo- 
graphic methods, 211-212 
Flight tests in aerial gunnery assess- 
ment 

photographic methods, 211-212 
University of Texas testing machine, 
210-211 

Four-bar linkage, 67-68 
counterbalancing, 68 
design, 67-68 

Frangible bullet training device, 212 
Franklin Institute tracking and ranging 
studies, 205-206 

Future of airborne fire-control systems, 
214-216 

assessment, 215-216 
computers, 214-215 
for guided bombs and rockets, 132 
planning and control, 216 
psychological design, 215 


^rONFlDE^^TLVL 


tracking controls, 214 
weapon development, 216 

General Electric remote control system 
for aerial gunnery, 199-201 
evaluation of system, 200 
free-gyro computing system, 199-200 
gyro-stabilized sight, 200 
sighting station shortcomings, 199- 
200 

standard B-29 computer faults, 199- 
200 

GRASP rocket sight, 134, 140-141 
altitude, 141 
components, 141 

development models, 134, 140-141 
glide angle input, 141 
Guided bomb control program activi- 
ties, 112-115 
AZON bomb, 112-114 
CARP sight, 114 
CRAB sight, 112-113 
ground-controlled bombing (GCB), 
115 

MIMO television comi)onent, 113- 
115 

Norden bombsight, 112-113 
RAZON bomb, 112-114 
ROC bomb, 113-115 
terminal collinearity, 113-114 
Guided bombs, control, 112-132 
bomber evasion, 121-122 
CARP sight, 124 
collinearity control, 119-121 
CRAB sight, 124 
first guiding sight, 122-123 
future, 132 

guiding simulator origin, 123-124 
interception course misunderstand- 
ing, 131 

])rogram activities, 112-115 
RAZON control from ground, 124- 
128 

television bomb (equations), 128-131 
trajectory analysis and synthesis, 
116-119 

Guided rockets, future, 132 
Gyros for angular rate bombing, 40-43, 
190-191 

Human factor (PUSS), 149-150 
Human factor in tracking 

see Tracking operator, human 

Instrumental components of airborne 
fire-control 

computation components, 20 
presentation of variables, 21 
primary data apparatus, 20-22 

Lead computation princi])les, 188-191 
angular rate, 190-191 
axis conversion, 191 
ballistic lead, 189-190 
electrical potentiometer method, 189 
gyroscope measurement methods, 
190-191 

kinematic lead, 15-16, 190-191 


INDEX 


247 


mechanical cam method, 189 
mechanical leakages, 189 
Lead-computing sights for aerial gun- 
nery, 180-181, 194-197 
angular rate error, 195 
British single-gyro sight (MK-II-C), 
181, 196 

Fairchild sights, 181, 197 
K-13 sight, 180-181 
Mark 14 giinsight, 195 
Mark 18 giinsight, 196 
Sperry K-3 sight, 180, 195 
Sperr}' K-4 sight, 180, 195 
Sperry K-12 sight, 195 
time-of-flight setting, 196 
tracking difficulty, 194 
transient effect, 194-195 
Linkages for computation and manipu- 
lation, 58, 66-78, 94 
applications of linkage computers, 71 
cams, 66 

complex functions, 70-71 
development methods, 67-70 
four-bar linkage, 67-68 
implicit range conversion, 94 
manipulation of moving mirror, 74-76 
mechanical linkage in simulation, 58 
orthopentax linkage, 72-78 
PUSS project, 72 
six-member linkage, 68-70 
trigonometric computations, 76 
types considered, 66-67 

Mathematical solution for aircraft tor- 
pedo aiming, 92-94 
Measurement of angular rate 

see Angular rates in airborne aiming 
controls 

Mechanical linkages 
see Linkages for computation and 
manipulation 

MIMO television component for ROC, 
113-115 

Miniature director Mark 32; 80-81 
■Miniature rocket sight (PARS), 135, 
143-145 

accelerometer component, 143 
skid problem, 144 
Models as development aid, 48-50 
developmental simulator, 48-49 
educational simulator, 49 
mathematical models, 49 
training simulator, 49 
Multiple sight indices in aiming con- 
trols, 29-30 

British LLBS Mark III, 29 
collision course, 30 
pilot’s universal sighting systems, 30 
Texas sight, 29 

Norden bombsight, 100, 112-113, 122 

Orthopentax linkage, 72-78 
applications to diverse fields, 76-78 
gnomon, 73-74, 77 

manipulation of moving mirror, 75-76 
trigonometric computations, 76 
Oscillatory cdptive gyro, 45-46 


Own-speed sights for aerial gunnery, 
193-194 

jam handy sight, 193 
K-10 Sperry sight, 193 
K-11 Sperry sight, 193 
K-13 Sperry sight, 194 

PACT toss bombing computer, 110-111 
155-156 

PARS miniature rocket sight, 135, 
143-145 

accelerometer component, 143 
skid problem, 144 

Photographic methods of flexible gun- 
nery assessment, 210-212 
Pilot’s universal sighting system (PUSS) 
aiming control, 150 
aiming control system, 135, 145-146 
capacitor in instrumental techniques, 
158-159 

components and systems, 153-157 
computer, 135, 145, 153-156 
dive bombing, 110-111 
future research, 145-146, 159-160 
glide angle, 155-157 
gyro, 43-44 

human factor, 149-150 
installation, 157 
linkages, 72 

multiple sight indices, 30 
PACT toss bombing computer, 155- 
156 

pneumatic components, 157-158 
roll-stabilization, 152-153 
sight head (PUSH), 150-152 
Plate feedback, 52 
Plotter, pursuit-collision course, 50 
Pneumatic components for pilot’s uni- 
versal sighting system (PUSS), 
157-158 

Position vector, 9-11 
Present range type torpedo directors, 
167-168 

Projectile aiming problem, 14-16 
Pursuit-collision course plotter, 50 
PUSH sight head, 151-152 
PUSS project 

see Pilot’s universal sighting system 

Radar, SCR 584; 124-125 
RASP rocket sight, 133, 137-140 
airspeed, 139 
altitude input, 137 
development models, 133, 140 
glide angle input, 139 
sighting component, 140 
target motion, correction, 139 
RAZON bomb 
collinearity control, 119 
CRAB sight, 112-113, 124 
differential analyzer solutions, 217- 
227 

guided bomb control program, 112- 
114 

RAZON bomb, control from ground, 
124-128 

radar control, 124-125 
rationalization based on vacuum 


confidential! 


flight conditions, 127-128 
visual control, 125-127 
Remote control systems for aerial gun- 
nery, 201-202 

Research recommendations 
see also Future of airborne fire-control 
systems 

guided rockets, 132 
pilot’s universal sighting system 
(PUSS), 145-146, 159-160 
simulation as development aid, 64-65 
Ring-and-bead sight, 179, 192 
ROC bomb, 61, 113-115 
CARP sight, 114, 124 
differential analyzer solutions for COR 
trajectories, 227-230 
television bomb controls (equations), 
128-131 

Rocket aiming from airplanes, 133-146 
aircraft rocket as weapon, 135-137 
future development, 145-146 
GRASP rocket sight, 134, 140-141 
PARS miniature rocket sight, 135, 
143-145 

Iirojects summary, 133-135 
PUSS computer, 135, 145 
RASP rocket sight, 133, 137-140 
Rocket sight, GRASP, 134, 140-141 
altitude, 141 
components, 141 

developmental models, 134, 140-141 
glide angle input, 141 
Rocket sight, PARS, 135, 143-145 
accelerometer component, 143 
skid problem, 144 
Rocket sight, RASP 
see RASP rocket sight 
Rockets, guided, 132 

SCR 584 radar, 124-125 
Sight head (PUSH), 151-152 
Sights 

aircraft rocket sight Mark 3; 135, 
143-145 

antisubmarine bombsight Mark 20, 
100-104 

CARP, 114, 124 
CRAB, 112-113, 124 
Draper/Davis (Army A-1), 110 
extrapolating antisubmarine bomb- 
sight, 100-106 

fixed sight systems, 192-193 
GRASP rocket, 134, 140-141 
gyro-stabilized (General Electric), 
200 

lead-computing, 180-181, 194-197 
Norden bombsight Mark 15; 100, 
112-113, 122 

optical reflector type, 192 
own-speed, 193-194 
PARS miniature rocket sight, 135, 
143-145 

RASP rocket, 133, 137-140 
ring-and-bead sight, 179, 192 ' 
Simulation, electronic 
see Electronic simulation 
Simulation as aerial gunnery assess- 
ment aid, 209 


248 


INDEX 


Simulation as development aid, 48-65 
airplane dynamics, 63-64 
electronic representation, 50-52 
feedback amplifiers, 52-54 
flare-bomb guiding, 58-61 
future development, 64-65 
mechanical linkage, 58 
mechanical simulator for tracking 
studies, 205 
models, 48-50 
nonlinear dynamics, 54-56 
supersimulator, 64-65 
television bomb guiding, 61-63 
time scale, 58 

Six-member linkage ‘ 

development plan, 68-69 
parametric curves, 69-70 

Space-time geometry in aiming process- 
es, 16-17 

Sperry remote control systems for aerial 
gunnery, 201-202 

Sperry sights 
K-3; 180, 195 
K-4; 180, 195 
K-10; 193 
K-11; 193 
K-12; 195 
K-13; 194 

Synchronous operations in aiming 
processes, 17-18 

Target approach, 12-13, 18-19 

circular-interception approach, 18-19 
collision course, 13 
proportional navigation, 18-19 
pursuit course, 12-13 

Target courses (aerial combat), 185- 
187 

Television bomb controls (equations), 
128-131 



Television bomb guiding simulation, 
61-63 

control dynamics, 62 
lead angle, 61 
“miss” assessment, 63 
operation, 61-62 
ROC bomb, 61 
scope presentation, 61 
underwater torpedo controls stabili- 
ty, 63 

Three-dimensional linkage (orthopen- 
tax) 

see Orthopentax linkage 
Torpedo aiming from airplanes, 79-94, 
163 

complete solution, 92-94 
conversion of present range as input, 
90-92 

development history, 79-83 
errors in target motion estimation, 
85-87 

linkage for implicit range conversion, 
94 

miniature director Mark 32; 80-81 
rule-of-thumb method, 163 
torpedo director Mark 30; 81 
two-man operated directors, 82, 87-90 
vectorial solution, 83-85 
Torpedo course stabilization, 165-166 
Torpedo director Mark 30; 81 
Torpedo director Mark 32; 80-81 
Torpedo directors, present range type, 
167-168 

Torpedo directors for aircraft 

see Torpedo aiming from airplanes 
Torpedo directors for use against evad- 
ing targets, 169-173 
construction plan, 173 
formulas for fictitious target angle, 
173 


lead angle solution, 171-173 
turning characteristics of ships, 169- 
171 

Toss bombing computer (PACT), 110- 
111, 155-156 

Tracking by manual means, 23-34 
aids, 27-28 

automatic regulators, 27-28 
causal loop, 24-26 

characteristics of higher order, 28- 
29 

complex dynamics, 28-29 
multiple sight indices, 29-30 
“natural” tracking, 23-24 
operational tracking circuit, 26-27 
pilot, 30-31 

Tracking operator, human, 30-34 
integrating response, 33 
lag factor in human response, 32- 
33 

linear operators, 31-32 
pilot, 30-31 

time-lag operator, 32-33 

Trajectory analysis, guided bombs, 116- 
119, 217-230 

Turret controls for bombers, 181-182 

Universal sight head for fighter pilots 
(PUSH), 150-152 

Universal sighting system 

see Pilot’s universal sighting system 
(PUSS) 

University of Texas testing machine, 
210-211 

Vectorial solution for aircraft torpedoes, 
83-85 

lead angle, 83-85 
moving target, 83 
torpedo speed vector, 83 




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